Question

log81/log27=x

Then what is the value of x..

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Answer 1

Answer:

4/3

Step-by-step explanation:

$\frac{ log(81) }{ log(27) } = x \\ \frac{ log( {3}^{4} ) }{ log( {3}^{3} ) } = x \\ \frac{4 log(3) }{3 log(3) } = x \\ \frac{4}{3} = x$

Answer 2

Given :

• $\tt\:\frac{log~81}{log~27}=x$

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To find :

• The value of x.

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Some formula to know while dealing with log problems :

❒ $\sf\:log_{a}(MN)=log_{a}M+log_{a}N$

❒ $\sf\:log_{a}(\frac{M}{N})= log_{a}M-log_{a}N$

❒ $\sf\:log_{a}M^{n}=nlog_{a}M$

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Solution :

$\tt\:\frac{log~81}{log~27}=x$

$\tt\:oR\:x=\frac{log~81}{log~27}$

• 81 = 3 × 3 × 3 × 3

• 27 = 3 × 3 × 3

$\tt:\implies\:x=\frac{log~3 \times 3 \times 3 \times 3}{log~3 \times 3 \times 3}$

$\tt:\implies\:x=\frac{log~3^{4}}{log~3^{3}}$

Using the third formula mentioned above

$\tt:\implies\:x=\frac{4~log~3}{3~log~3}$

$\tt:\implies\:x=\frac{4}{3}$

$\small{\underline{\boxed{\mathrm{:\implies\:x=1\frac{1}{3}}}}}$ ★

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Henceforth the required value of x -

$\:~~~~~~~~~~~~~~~~~~~~$ $\bf\dag$ $\bf\color{cyan}{\:\frac{4}{3}~oR~1\frac{1}{3}}$

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