Question 1005203

Find the exact solution, using common logarithms. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

4^(2x + 3) = 5^(x - 2)

Find a two-decimal-place approximation of each solution. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
<pre>{{{4^(2x + 3) = 5^(x - 2)}}}
{{{log ((4^(2x + 3))) = log ((5^(x - 2)))}}} -------- Taking the log of both sides
{{{(2x + 3) * log (4) = (x - 2) * log (5)}}} -------- Applying {{{log a^b = a * log (b)}}} 
{{{(2x + 3)/(x - 2) = log (5)/log (4)}}}
{{{(2x + 3)/(x - 2) = 1.160964047}}}
2x + 3 = 1.160964047(x - 2) -------- Cross-multiplying
2x + 3 = 1.160964047x - 2.321928
2x - 1.160964047x = - 2.321928 - 3
.839035953x = - 5.321928
{{{x = (- 5.321928)/.839035953}}}, or {{{highlight_green(x = -6.342908285)}}}