SOLUTION: Solve the exponential equation using logarithms. Give the answer in decimal form, rounding to four decimal places. (Enter your answers as a comma-separated list.) 5^x^2 = 2^5x

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the exponential equation using logarithms. Give the answer in decimal form, rounding to four decimal places. (Enter your answers as a comma-separated list.) 5^x^2 = 2^5x      Log On


   

Question 891480: Solve the exponential equation using logarithms. Give the answer in decimal form, rounding to four decimal places. (Enter your answers as a comma-separated list.)
5^x^2 = 2^5x
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
5^x^2 = 2^5x
I can't tell whether that means

%285%5Ex%29%5E2%22%22=%22%222%5E%285x%29 or matrix%282%2C1%2C%22%22%2C5%5E%28x%5E2%29%29matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29matrix%282%2C1%2C%22%22%2C2%5E%285x%29%29

If it's the first way:

5%5E%282x%29%22%22=%22%222%5E%285x%29

ln%285%5E%282x%29%29%22%22=%22%22ln%282%5E%285x%29%29

2x%2Aln%285%29%22%22=%22%225x%2Aln%282%29

2x%2Aln%285%29%22%22-%22%225x%2Aln%282%29 %22%22=%22%22 %220%22

x%282ln%285%29%2B5ln%282%29%29  %22%22=%22%22 %220%22

Divide both sides by 2ln%285%29%2B5ln%282%29

x%22%22=%22%22%220%22

------------------------

If it's the second way,

matrix%282%2C1%2C%22%22%2C5%5E%28x%5E2%29%29matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29matrix%282%2C1%2C%22%22%2C2%5E%285x%29%29

matrix%282%2C1%2C%22%22%2Cln%285%5E%28x%5E2%29%29%29matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29matrix%282%2C1%2C%22%22%2Cln%282%5E%285x%29%29%29

%28x%5E2%29ln%285%29%22%22=%22%225x%2Aln%282%29

%28x%5E2%29ln%285%29%22%22-%22%225x%2Aln%282%29%22%22=%22%22%220%22

x%2A%28x%2Aln%285%29-5ln%282%29%29%22%22=%22%22%220%22

x=0;  x%2Aln%285%29-5%2Aln%282%29=0

          x%2Aln%285%29=5%2Aln%282%29

          x=5%2Aln%282%29%2Fln%285%29

          x=2.15338279

Answers:   0, 2.1534 (rounded to four decimal places).

Edwin