Question 275956
{{{(log(2, (25)))(log(x, (16)))=4}}}
Equations with logarithms are easier to work with and solve when the bases of the logarithms are the same. So we'll start by using the change of base formula, {{{log(a, (p)) = log(b, (p))/log(b, (a))}}}, to change the base of one of the logarithms. Changing the base of the base x logarithm to base 2 looks promising to me because 16 is a power of 2:
{{{(log(2, (25)))(log(2, (16))/log(2, (x)))=4}}}
Since {{{2^4 = 16}}}, {{{log(2, (16)) = 4}}}. Substituting this in we get:
{{{(log(2, (25)))(4/log(2, (x)))=4}}}
Multiplying we get:
{{{(4log(2, (25)))/log(2, (x))=4}}}
Multiplying both sides by {{{log(2, (x))}}} we get:
{{{4log(2, (25))=4log(2, (x))}}}
Dividing both sides by 4 we get:
{{{log(2, (25))=log(2, (x))}}}
So x must be 25!