SOLUTION: Hi! {{{4^x-10*2^(x-1)=24}}} PS! the answer is x=3, but dont know how to achieve it. Thanks Richard

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hi! {{{4^x-10*2^(x-1)=24}}} PS! the answer is x=3, but dont know how to achieve it. Thanks Richard      Log On


   

Question 728524: Hi!
4%5Ex-10%2A2%5E%28x-1%29=24
PS! the answer is x=3, but dont know how to achieve it.
Thanks
Richard
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
4%5Ex-10%2A2%5E%28x-1%29=24..write 2%5E%28x-1%29 as 2%5Ex%2F2 and 4%5Ex as 2%5E%282x%29
2%5E%282x%29-10%2A2%5Ex%2F2=24

2%5E%282x%29-cross%2810%295%2A2%5Ex%2Fcross%282%29=24........2%5E%282x%29=2%5E%28x%292%5E%28x%29

2%5Ex%2A2%5E%28x%29-5%2A2%5Ex=24
2%5Ex%2A%282%5Ex-5%29=24....true if and only if 2%5Ex=8
than we have
2%5Ex=2%5E3...=>..if bases same, exponents are same too...so, x=3