Question

please explain this question. ​

Answer 1

Answer

$\mathtt{Value\: of \: m\: is \: 24}$

Solution

$log_{8}(m) \: + \: log_{8}( \frac{1}{6} ) \: = \: \frac{2}{3}$

Some formulae used in this question are :-

$\boxed{ \boxed {log(a) \: + \: log(b) \: = log(a.b) }}$

$\boxed{ \boxed{ log_{a}(c ) \: = \: b \: then}} \: \\ \boxed{ \boxed{ c \: = \: {a}^{b}}}$

Using these formulae

$\implies \: log_{8}(m \times \frac{1}{6} ) \: = \: \frac{2}{3}$

$\implies \: log_{8}( \frac{m}{6} ) \: = \: \frac{2}{3}$

Removing Log from the equation –

$\implies \: \frac{m}{6} \: = \: {8}^{ \frac{2}{3} }$

We know that 8 = ( 2)³

$\implies \: \frac{m}{6} \: = \: {2}^{ \frac{2}{3} \times 3}$

Now simplifying the power of 2

$\implies \: \frac{m}{6} \: = \: {2}^{2}$

$\implies \: m \: = \: 4 \times 6$

$\boxed{ \boxed{ \implies \: m \: = \: 24}}$

So the value of m = 24

Answer 2

$\large \underline{ \green{ \boxed{ \bf \blue{Required \: Answer}}}}$