Question 600334
{{{log(16,(32))=x+3}}} Start with the given equation



{{{log(16,(32))-3=x}}} Subtract 3 from both sides



{{{x = log(16,(32))-3}}} Flip the equation



{{{x = (log(10,(32)))/(log(10,(16)))-3}}} Expand the log using the change of base formula.



{{{x = (log(10,(2^5)))/(log(10,(2^4)))-3}}} Rewrite 32 as {{{2^5}}} and 16 as {{{2^4}}}



{{{x = (5*log(10,(2)))/(4*log(10,(2)))-3}}} Pull down the exponents.



{{{x = 5/4-3}}} Divide and cancel out like terms.



{{{x = -7/4}}} Combine the fractions.



So the exact solution is {{{x = -7/4}}}