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 .
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}
(i) log x + log 5 = 2 log 3
\text { Given } 2 \log _{10} x+1=\log _{10} 250, \text { find }
\text { If } \log x / \log 5=\log y^{2} / \log 2=\log 9 / \log (1 / 3), \text { find } x \text { and } y .
Solve the following equations:
\text { (vii) } \log (3 x+2)+\log (3 x-2)=5 \log 2
Solve for x:
\log _{3}(x+1)-1=3+\log _{3}(x-1)
. Solve for x:
5^{\ln x}+3^{\log x}=3^{\log x+1}-5^{\log x-1}
\text { If } \log (x-y) / 2=1 / 2(\log x+\log y), \text { prove that } x^{2}+y^{2}=6 x y
\text { If } x^{2}+y^{2}=23 x y, \text { Prove that } \log (x+y) / 5=1 / 2(\log x+\log y)
\text { If } p=\log _{10} 20 \text { and } q=\log _{10} 25, \text { find the value of } x \text { if } 2 \log _{10}(x+1)=2 p-q
. Show that:
Prove the following identities:
\text { Given that } \log _{a} x=1 / a, \log _{b} x=1 / \beta, \log _{c} x=1 / \gamma, \text { find } \log _{a b c} x
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