SOLUTION: Solve the equation. Find the exact solution if possible; otherwise, use a calculator to approximate to four decimals. {{{ 5^(x+2)=e^(2x)}}} *Note: e=base of the natural

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the equation. Find the exact solution if possible; otherwise, use a calculator to approximate to four decimals. {{{ 5^(x+2)=e^(2x)}}} *Note: e=base of the natural       Log On


   

Question 805152: Solve the equation. Find the exact solution if possible; otherwise, use a calculator to approximate to four decimals.
+5%5E%28x%2B2%29=e%5E%282x%29

*Note: e=base of the natural logarithm.
Thanks so much!!
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
+5%5E%28x%2B2%29=e%5E%282x%29

ln%285%5E%28x%2B2%29%29=ln%28e%5E%282x%29%29
%28x%2B2%29%2Aln%285%29=2x%2A1
x%2Aln%285%29%2B2%2Aln%285%29=2x
2%2Aln%285%29=2x-x%2Aln%285%29
2%2Aln%285%29=x%282-ln%285%29%29
highlight%28x=%282%2Aln%285%29%29%2F%282-ln%285%29%29%29

You can replace ln(5) with 1.6094 and compute using a calculator.