M l aggarwal understanding icse mathematics class 9 Solutions for Chapter 9 logarithms

Exercises in Chapter 9 logarithms Grade 9

Logarithms Exercise 9.1

Logarithms Exercise 9.2

Questions in Logarithms Exercise 9.1

Convert the following to the logarithmic form:

Convert the following into the exponential form:

By converting to exponential form, find the values of:

Solve the following equations for x:

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

$\text { Given } \log _{10} x=a, \log _{19} y=b \text { and } \log _{10} z=c$

$\text { (iii) if } \log _{10} P=2 a+b / 2-3 c, \text { express } P \text { in terms of } x, y \text { and } z$

$\text { If } \log _{10} x=a \text { and } \log _{10} y=b, \text { find the value of } x y .$

$\text { Given } \log _{10} \mathrm{a}=\mathrm{m} \text { and } \log _{10} \mathrm{b}=\mathrm{n}, \text { express } \mathrm{a}^{3} / \mathrm{b}^{2} \text { in terms of } \mathrm{m} \text { and } \mathrm{n} .$

$\text { Given } \log _{10} a=2 a \text { and } \log _{10} y=-b / 2$

$\text { If } \log _{2} y=x \text { and } \log _{3} z=x, \text { find } 72^{x} \text { in terms of } y \text { and } z .$

$\text { If } \log _{2} x=a \text { and } \log _{8} y=a, \text { write } 100^{2 n-1} \text { in terms of } x \text { and } y .$

Questions in Logarithms Exercise 9.2

Simplify the following:

Evaluate the following:

Express each of the following as a single logarithm:

Prove the following:

$\text { If } x=(100)^{n}, y=(10000)^{b} \text { and } z=(10)^{c}, \text { express } \log \left[(10 \sqrt{y}) / x^{2} z^{3}\right] \text { in terms of } a, b, c$

$\text { If a }=\log _{10} x, \text { find the following in terms of a : }$

$\text { If } a=\log 2 / 3, b=\log 3 / 5 \text { and } c=2 \log \sqrt{(5 / 2)} \text { . Find the value of }$

$\text { If } x=\log 3 / 5, y=\log 5 / 4 \text { and } z=2 \log \sqrt{3 / 2}, \text { find the value of }$

$\text { If } \log \mathbf{V}+\log 3=\log \pi+\log 4+3 \log r, \text { find } \mathbf{V} \text { in terms of other quan tities. }$

$\text { Given } 3(\log 5-\log 3)-(\log 5-2 \log 6)=2-\log n, \text { find } n .$

$\text { Given that log }_{10} \mathrm{y}+2 \mathrm{log}_{10} \mathrm{x}=2, \text { express y in terms of } \mathrm{x} .$

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

$\text { If } a^{2}=\log _{10} x, b^{2}=\log _{10} y \text { and } a^{2} / 2-b^{2} / 3=\log _{10} z . \text { Express } z \text { in } \operatorname{term} s \text { of } x \text { and }$

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

Given that log x = m + n and log y = m – n, express the value of $\left(10 x / y^{2}\right)$

in terms of m and n.

$\text { If } \log _{5} / 2=\log y / 3, \text { find the value of } y^{4} / x^{6}$