Question

If log8 x + log8 (1/6) = 1/3 then the value of x is:

Answer 1

Answer:

The value of x is 12.

Step-by-step explanation:

Given : If $\log_8 x+\log_8(\frac{1}{6})=\frac{1}{3}$

To find : The value of x?

Solution :

Expression  $\log_8 x+\log_8(\frac{1}{6})=\frac{1}{3}$

When bases are same then according to logarithmic property,

$\log a+\log b=\log (ab)$

$\log_8(\frac{x}{6})=\frac{1}{3}$

Using property, $\log_b a=x\\\Rightarrow a=b^x$

$\frac{x}{6}=8^{\frac{1}{3}}$

$\frac{x}{6}=2$

$x=2\times 6$

$x=12$

Therefore, The value of x is 12.

Answer 2

Answer:

$The \: value \: of \: x = 12$

Step-by-step explanation:

$Given \:log_{8}x+log_{8}\:\frac{1}{6}=\frac{1}{3}$

$\implies log_{8}\:{x \times \frac{1}{6}}=\frac{1}{3}$

$By \: logarithmic\:law:\\log_{a}m+log_{a}n= log_{a}mn$

$\implies log_{8}\:\frac{x}{6}=\frac{1}{3}$

$\implies \frac{x}{6}=8^{\frac{1}{3}}$

$Since, If \: log_{a}N = x \:\implies N = a^{x}$

$\implies x = 6 \times \big(2^{3}\big)^{\frac{1}{3}}$

$\implies x = 6 \times 2$

$\implies x = 12$

Therefore,

$The \: value \: of \: x = 12$

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