Question

if a=b squere =c cube then log ab base c =

Answer 1

Please see the attachment

Answer 2

The value of

$log_{c}(ab) = \frac{9}{2}$

GIVEN

Mathematical expression -

$a = {b}^{2} = {c}^{3}$

TO FIND

The value of

$log_{c}(ab)$

SOLUTION

We can simply solve the above problem as follows-

By taking

$log_{c}$

$log_{c}(a) = log_{c}( {b}^{2} ) = log_{?}( {c}^{3} )$

We know that,

$log( {a}^{n} ) = n log(a)$

Therefore,

$log_{c}(a) = 2 log(b)$

And,

$2 log_{c}(b) = 3$

Because

$log_{c}(c) = 1$

Therefore,

$log_{c}(a) = 3$

And,

$log_{c}(b) = \frac{3}{2}$

We know that,

$log_{c}(ab) = log_{c}(a) + log_{c}(b)$

Putting the values in the above equation we get,

$log_{c}(ab) = 3 + \frac{3}{2} = \frac{9}{2}$

Hence The value of

$log_{c}(ab) \: is \: \frac{9}{2}$

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