SOLUTION: Solve the following logarithmic equations a) log5(8−7x)=3 b) 5^x+2=4^1−x

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the following logarithmic equations a) log5(8−7x)=3 b) 5^x+2=4^1−x      Log On


   

Question 960951: Solve the following logarithmic equations
a) log5(8−7x)=3
b) 5^x+2=4^1−x
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

a)
log%285%2C%288-7x%29%29=3.......change to base 10
log%28%288-7x%29%29%2Flog%285%29=3

log%28%288-7x%29%29=3log%285%29
log%28%288-7x%29%29=log%285%5E3%29
log%28%288-7x%29%29=log%28125%29..........if log same, then
8-7x=125.....solve for x
7x-8%2B125=0
7x%2B117=0
7x=-117
x=-117%2F7

b)
5%5E%28x%2B2%29=4%5E%281-x%29..........take log of both sides
log%285%5E%28x%2B2%29%29=log%284%5E%281-x%29%29
%28x%2B2%29log%285%29=%281-x%29log%284%29
x%2Alog%285%29%2B2log%285%29=log%282%5E2%29-x%2Alog%282%5E2%29
x%2Alog%285%29%2Bx%2A2log%282%29=2log%282%29-2log%285%29
x%28log%285%29%2B2log%282%29%29=2%28log%282%29-log%285%29%29
x+=+%282+%28log%282%29-log%285%29%29%29%2F%282+log%282%29%2Blog%285%29%29