SOLUTION: How do I solve the equation, {{{ log(9, (b+4)) - log(9, (b-3)) = log(9, 8) }}}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How do I solve the equation, {{{ log(9, (b+4)) - log(9, (b-3)) = log(9, 8) }}}      Log On


   

Question 6629: How do I solve the equation, +log%289%2C+%28b%2B4%29%29+-+log%289%2C+%28b-3%29%29+=+log%289%2C+8%29+
Answer by prince_abubu(198) About Me  (Show Source):
You can put this solution on YOUR website!
First up, use the property +log%28b%2Ca%29+-+log%28b%2Cc%29+=+log%28b%2C%28a%2Fc%29%29+.

So using that, +log%289%2C%28%28b%2B4%29%2F%28b-3%29%29%29+=+log%289%2C8%29+

Since both sides of the equation are log base 9, we can simply say

+%28b%2B4%29%2F%28b-3%29+=+8+

+b+%2B+4+=+8%28b+-+3%29+ <---- multiply both sides by (b-3)

+b+%2B+4+=+8b+-+24+ <---- Solve for b

+28+=+7b+ <----- combine like terms across equals sign

+b+=+4+ <---- finally solve for b