SOLUTION: Solve for x in the equation 5^(2x+3)-6(5^x )=595

Algebra ->  Finance -> SOLUTION: Solve for x in the equation 5^(2x+3)-6(5^x )=595      Log On


   

Question 1195397: Solve for x in the equation 5^(2x+3)-6(5^x )=595
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


5%5E%282x%2B3%29-6%285%5Ex+%29=595

The equation involves 5 to the powers (2x+3) and x. Rewrite the equation as a "quadratic" with "variable" 5^x by writing 5%5E%282x%2B3%29 as %285%5E3%29%285%5E%282x%29%29.

125%285%5E%282x%29%29-6%285%5Ex%29-595=0

The quadratic does not factor over the integers; a graphing calculator shows

5%5Ex=2.2058744 to several decimal places. Then

x%2Alog%285%29=log%282.2058744%29
x=log%282.2058744%29%2Flog%285%29=0.4915529686 again to several decimal places.

ANSWER: x = approximately 0.4915529686