Question 144486
{{{log(2,(x - 2)) + 5 = 8 - log(2,( 4))}}} Start with the given equation



{{{log(2,(x - 2)) + 5 = 8 - 2}}} Evaluate {{{log(2,( 4))}}} to get 2



{{{log(2,(x - 2))  = 8 - 2-5}}} Subtract 5 from both sides



{{{log(2,(x - 2))  = 1}}} Combine like terms



{{{x - 2  = 2^1}}} Rewrite the logarithmic equation into an exponential equation



{{{x - 2  = 2}}} Raise 2 to the first power to get 2



{{{x  = 4}}} Solve for x




So our answer is {{{x  = 4}}}