SOLUTION: Solve the following equation. Show all work. {{{2^(5x)*16^(1-x)=4^(x-3)}}}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the following equation. Show all work. {{{2^(5x)*16^(1-x)=4^(x-3)}}}      Log On


   

Question 317476: Solve the following equation. Show all work.
2%5E%285x%29%2A16%5E%281-x%29=4%5E%28x-3%29
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

2%5E%285x%29%2A16%5E%281-x%29=4%5E%28x-3%29

Write 16 as %282%5E4%29 and write 4 as %282%5E2%29

2%5E%285x%29%2A%282%5E4%29%5E%281-x%29=%282%5E2%29%5E%28x-3%29

Remove the parentheses by multiplying the inner exponents by
the outer exponents:

2%5E%285x%29%2A2%5E%284%2A%281-x%29%29=2%5E%282%2A%28x-3%29%29

Distribute in the exponents:

2%5E%285x%29%2A2%5E%284-4x%29=2%5E%282x-6%29

Add the exponents of 2 on the left:

2%5E%285x%2B4-4x%29=2%5E%282x-6%29

2%5E%28x%2B4%29=2%5E%282x-6%29

The bases are the same and are positive and not 1, so
we may set the exponent of 2 on the left equal the exponent
of 2 on the right:

x%2B4=2x-6
10=x

Edwin