Question

Express 1/343=3c in logarithmic form

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Answer 1

Given:

The equation is

$\dfrac{1}{343}=3^c$

To find:

The logarithmic form of given equation.

Solution:

We have,

$\dfrac{1}{343}=3^c$

$\dfrac{1}{7^3}=3^c$

$7^{-3}=3^c$        $[\because a^{-n}=\dfrac{1}{a^n}]$

Taking log on both sides.

$\log 7^{-3}=\log 3^c$

$-3\log 7=c\log 3$        $[\because \log x^n=n\log x]$

$\dfrac{-3\log 7}{\log 3}=c$

Therefore, the required equation is $c=\dfrac{-3\log 7}{\log 3}$.