Question

Find the base when logarithm of 32 is 15

Answer 1

Let the base be having a value of x.

Now,

According to the question,

$log_{x} 32 = 15$

So it basically means that which number when raised to  15th power gives 32.

so,

$x^{15} =32$

Let's try to equate the power first so that we can get a matching base,

(The method is not very effective in all cases but we have an easier one here so it's gonna work)

$x^{15} =2^{5} =2^{\frac{15}{3} } = 2^{(\frac{1}{3})15}$

Comparing both sides we get the answer as 2^(1/3).