Selina solutions concise maths class 9 icse Solutions for Chapter 8 chapter 8 logarithms

Exercises in Chapter 8 chapter 8 logarithms Grade 9

Exercise 8(A)

Exercise 8(B)

Exercise 8(C)

Exercise 8(D)

Questions in Exercise 8(A)

Express each of the following in exponential form:

$\begin{aligned} &\text { (i) }\\ &\log _{8} 0.125=-1 \end{aligned}$

$\begin{aligned} &\text { (ii) }\\ &\log _{10} 0.01=-2 \end{aligned}$

$\begin{aligned} &\text { (iii) }\\ &\log _{4} A=x \end{aligned}$

$\begin{aligned} &(\mathrm{v})\\ &\log _{10} 1=0 \end{aligned}$

$\begin{aligned} &\text { Solve for } \mathrm{x} \text { : }\\ &\log _{10} x=-2 \end{aligned}$

Find the logarithm of:

State, true or false:

Find x if:

Evaluate:

$\text { If } \log _{\mathrm{a}} \mathrm{m}=\mathrm{n}, \text { express } \mathrm{a}^{n-1} \text { in terms of } \mathrm{a} \text { and } \mathrm{m}$

$\text { Given } \log _{2} x=m \text { and } \log _{5} y=n$

$\text { (i) Express } 2^{m-3} \text { in terms of } x .$

$\text { (ii) Express } 5^{3 n+2} \text { in terms of } y \text { . }$

$\text { If } \log _{2} x=a \text { and } \log _{5} y=a, \text { write } 72 \text { in terms of } x \text { and } y .$

$\text { Solve for } x: \log (x-1)+\log (x+1)=\log _{2} 1$

$\text { If } \log \left(x^{2}-21\right)=2, \text { show that } x=+11$

Questions in Exercise 8(B)

$\begin{aligned} &\text { If } \log _{10} 8=0.90 ; \text { find the value of: }\\ &\text { (i) } \log _{10} 4 \end{aligned}$

$\text { (ii) } \log \sqrt{32}$

$\begin{array}{ll} \text { (iii) } & \log 0.125 \end{array}$

Express in terms of log 2 and log 3.

Express each of the following in a form free from logarithm:

(i) 2logx-logy=1

(ii) 2logx+3logy=loga

(iii) alogx-blogy=2log3

Evaluate each of the following without using tables:

$\begin{aligned} &\text { Prove that: }\\ &2 \log \frac{15}{18}-\log \frac{25}{162}+\log \frac{4}{9}=\log 2 \end{aligned}$

$\begin{aligned} &\text { Find } x, \text { if: }\\ &x-;\log 48+3 \log 2=\frac{1}{3} \log 125-\log 3 \end{aligned}$

$\text { Express } \log _{10} 2+1 \text { in the form of } \log _{10} x$

Solve for x:

$\text { Given } \log x=m+n \text { and } \log y=m-n, \text { express the value of } \log \frac{10 x}{a^{2}} \text { in terms of } m \text { and }$ n

State, true or false:

$\begin{aligned} &\text { (i) }\\ &\log 1 \times \log 1000=0 \end{aligned}$

$\begin{array}{l} \text { (ii) } \\ \qquad \frac{\log x}{\log y}=\log x-\log y \end{array}$

$\begin{aligned} &\text { (iii) } \quad \text { If, }\\ &\frac{\log 25}{\log 5}=\log x \text { , then } x=2 \end{aligned}$

$\begin{aligned} &\text { (iv) }\\ &\log x+\log y=\log x \times \log y \end{aligned}$

$\text { If } \log _{10} 2=a \text { and } \log _{10} 3=b ; \text { express each of the following in terms of }{ }^{6} a^{\prime} \text { and }{ }^{\prime} b^{\prime}:$

$\text { (i) } \log 12$

$\text { (ii) } \log 2.25$

$\text { (iii) } \log 2 \frac{1}{4}$

$(\mathrm{iv}) \quad \log 5.4$ $\text { iv }) \quad \log 60$

$\text { (vi) } \log 3 \frac{1}{8}$

If log 2= 0.3010 and 0.4771; find the value of:

(i) log 12

(ii) log 1.2

(iii) log 3.6

(iv) log 15

(v) log 25

$\text { (vi) } \frac{2}{3} \log 8$

$\text { Given: } 2 \log _{10} x+1=\log _{10} 250 \text { , find: }$

(i) x

$\text { (ii) } \log _{10} 2 x$

Given $3 \log x+\frac{1}{2} \log y=2 \text { , express } y \text { in terms of } x$

$\text { If } x=(100)^{a}, y=(10000)^{b} \text { and } z=(10)^{\circ}, \text { find } \quad \log \frac{10 \sqrt{y}}{x^{2} z^{3}} \text { in terms of } a, b \text { and } c$

If 3(log5-log3)-(log5-2log6)=2-logx, find x.

Questions in Exercise 8(C)

If log 27=1.431, find the value of:

(i) log 9

(ii) log 300

$\text { If } \log _{10} a=b, \text { find } 10^{3 b-2} \text { in terms of a. }$

$\text { If } \log _{5} x=y, \text { find } 5^{2 x+3} \text { in terms of } x$

$\begin{aligned} &\text { Given: } \log _{3} m=x \text { and } \log _{3} n=y\\ &\text { (i) Express } 3^{2 x-3} \text { in terms of } m \text { . } \end{aligned}$

$\text { (ii) Write down } 3^{1-2 y+3 x} \text { in terms of } m \text { and } n$ $\text { (iii) } \text { If } 2 \log _{3} A=5 x-3 y ; \text { find } A \text { in terms of } m \text { and } n$

Simplify:

$\begin{array}{l} \text { (i) } \\ \qquad \log (a)^{3}-\log a \end{array}$

$\begin{aligned} &\text { (ii) }\\ &\log (a)^{3}+\log a \end{aligned}$

If log (a+b)=log a + log b, find a in terms of b.

Prove that:

$(\text { i }) \quad(\log a)^{2}-(\log b)^{2}=\log (a / b) \cdot \log (a b)$

$\text { (ii) } \quad \text { If } a \log b+b \log a^{-1}=0, \text { then } b^{a} \cdot a^{b}=10$

(i) If log (a+1)=log (4a-3)-log3; find a.

(ii) If 2logy-logx-3=0, express x in terms of y.

Given log x=2m-n, log y=n-2m and log z=3m-2n, find in terms of m and n, the value of:

$\text { Given } \log _{x} 25-\log _{x} 5=2-\log _{x}(1 / 125) ; \text { find } x$

Questions in Exercise 8(D)

$\begin{aligned} &\text { If }\\ &\frac{3}{2} \log a+\frac{2}{3} \log b-1=0 \text { find the value of } a^{9} . b^{4} \end{aligned}$

If x=1+log2-log5, y=2log3 and z=loga-log5; find the value of a, if x=y=2z.

If x=log 0.6; y=log 1.25 and z=log 3-2 log 2, find the values of:

(i) x+y-z

(ii) $5^{x+y-2}$

$\text { If } a^{2}=\log x, b^{3}=\log y \text { and } 3 a^{2}-2 b^{3}=6 \log z, \text { express } y \text { in terms of } x \text { and } z$

$\text { If } \log \frac{a-b}{2}=\frac{1}{2}(\log a+\log b), \text { show that } a^{2}+b^{2}=6 a b$

$\text { If } a^{2}+b^{2}=23 a b, \text { show that: }$

If m=log20 and n=log 25, find the value of x, so that: 2log(x-4)=2m-n.

Solve for x and y; if x>0 and y>0:

$\log x y=\log \left(\frac{x}{y}\right)+2 \log 2=2$

Find x, if:

$\begin{aligned} &\text { (i) }\\ &\log _{x} 625=4 \end{aligned}$

$\begin{aligned} &\text { (ii) }\\ &\log _{x}(5 x-6)=2 \end{aligned}$

If p=log 20 and q=log 25, find the value of x, if 2 log (x+1) = 2p-q.

$\text { If } \log _{2}(x+y)=\log _{3}(x-y)=\frac{\log 25}{\log 0.2}, \text { find the values of } x \text { and } y$

$\text { Given: } \frac{\log x}{\log y}=\frac{3}{2} \text { and } \log (x y)=5 ; \text { find the values of } x \text { and } y$

$\begin{aligned} &\text { Given } \log _{10} x=2 a \text { and } \log _{10} y=\frac{b}{2}\\ &\text { (i) Write } 10^{\circ} \text { in terms of } \mathrm{x} \end{aligned}$

$\text { (ii) Write } 10^{2 b+1} \text { in terms of } y$

$\text { (iii) } \quad \text { If } \log _{10} P=3 a-2 b, \text { express } P \text { in terms of } x \text { and } y .$

$Solve: $$ \log _{5}(x+1)-1=1+\log _{5}(x-1) $$$

Solve for x, if:

$\log _{x} 49-\log _{x} 7+\log _{x} \frac{1}{343}=-2$

$\begin{array}{l} \text { If } a^{2}=\log x, b^{3}=\log y \text { and } \\ \frac{a^{2}}{2}-\frac{b^{3}}{3}=\log c \text { , find } c \text { in terms of } x \text { and } y . \end{array}$

$\begin{aligned} &\text { Given } x=\log _{10} 12, y=\log _{4} 2 x \log _{10} 9 \text { and } z=\log _{10} 0.4, \text { find: }\\ &\text { (i) } x-y-z \end{aligned}$

$\text { (ii) } 13^{x-y-2}$

$\begin{aligned} &\text { Solve for } \mathrm{x}\\ &\log _{x} 15 \sqrt{5}=2-\log _{x} 3 \sqrt{5} \end{aligned}$

Evaluate:

$(i) \log _{b} a \times \log _{e} b \times \log _{a} c$

$(i i) \log _{3} 8 \div \log _{9} 16$

$\text { (iii) } \frac{\log _{5} 8}{\log _{25} 16 \times \log _{100} 10}$

Show that:

$\log _{a} m \div \log _{a b} m$ $=1+\log b$

$\log _{\sqrt{27}} x=2 \frac{2}{3}, \text { find }$

$\begin{aligned} &\text { Evaluate: }\\ &\frac{1}{\mid o g_{a} b c+1}+\frac{1}{\mid o g_{b} c a+1}+\frac{1}{\mid o g_{c} a b+1} \end{aligned}$