SOLUTION: Thanks in advance - this is the last question on my homework and I can't figure it out. Solve for x 10^(2x-1)= e^(4x-3)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Thanks in advance - this is the last question on my homework and I can't figure it out. Solve for x 10^(2x-1)= e^(4x-3)      Log On


   

Question 79204: Thanks in advance - this is the last question on my homework and I can't figure it out. Solve for x
10^(2x-1)= e^(4x-3)
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x
10^(2x-1)= e^(4x-3)
ln%2810%5E%282x-1%29%29=ln%28e%5E%284x-3%29%29
you can either take the common log, or the natural log of both sides. I chose natural log so that I didn't have to deal with e as a number.
%282x-1%29ln%2810%29=%284x-3%29ln%28e%29 ln(e)=1
%282x-1%29ln%2810%29=4x-3 distribute ln(10)
2xln%2810%29-ln%2810%29=4x-3 Get x's to one side of = sign.
2xln%2810%29-4x-ln%2810%29=4x-4x-3 get things without x's to the other side.
2xln%2810%29-4x-ln%2810%29%2Bln%2810%29=ln%2810%29-3
2xln%2810%29-4x=ln%2810%29-3 factor out the x's
x%282ln%2810%29-4%29=ln%2810%29-3 divide by the coefficient of x
x%282ln%2810%29-4%29%2F%282ln%2810%29-4%29=%28ln%2810%29-3%29%2F%282ln%2810%29-4%29
x=%28ln%2810%29-3%29%2F%282ln%2810%29-4%29 Put it in your calculator.
x=-1.15243
Happy Calculating!!!!