Question

op
If
log 8 (3) = X to log 2(3), then x?
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Answer 1

$\huge{ \underline{ \underline{ \green{ \sf{ Detailed \: Answer :}}}}}$

• To find : The value of x ,if

$log_{8}(3) = x \: log_{2}(3)$

${\red{\boxed{\large{\bold{Properties \: of \: Logarithm }}}}}$

$log_{a {}^{c} }(b) = \frac{1}{c} log_{a}(b)$

$log_{a}(b {}^{n} ) = n log_{a}(b)$

${\red{\huge{\underline{\mathbb{Answer:-}}}}}$

$log_{8}( 3) = x \: log_{2}(3)$

$log_{2 {}^{3} }(3) = x \: log_{2}(3)$

By using properties of logarithm

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$\frac{1}{3} log_{2}(3) = x \: log_{2}(3)$

on comparing LHS and RHS it is clear that ; the value of x is

${\purple{\boxed{\large{\bold{x =\frac{1}{3}}}}}}$

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More properties of logarithm

• log a + log b = log (ab)
• log a - log b = log (a/b)