SOLUTION: What is the solution to the following indicial equations? {{{ 5^(x+2) = 8.5 }}} {{{ 6.5^x=8.4^(4x-10) }}}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: What is the solution to the following indicial equations? {{{ 5^(x+2) = 8.5 }}} {{{ 6.5^x=8.4^(4x-10) }}}      Log On


   

Question 252804: What is the solution to the following indicial equations?
+5%5E%28x%2B2%29+=+8.5+
+6.5%5Ex=8.4%5E%284x-10%29+
Answer by JimboP1977(311) About Me  (Show Source):
You can put this solution on YOUR website!
Using log base 10
+log+5%5E%28x%2B2%29+=+log+8.5
+%28x%2B2%29%2A+log+5+=+log+8.5
+%28x%2B2%29=+log+%288.5%29%2Flog+5
+x=+%28log+%288.5%29%2Flog+5%29-2
x=+-0.67 2 d.p.
|
x%2A+log+6.5=+%284x-10%29%2Alog+8.4+
x=+%284x-10%29%2Alog+8.4%2Flog+6.5+
x=+%284x-10%29%2A1.137+
x=+%284.548x-11.37%29
11.37=+%283.548x%29
3.2046+=+x 4.dp.
All a bit messy. There probably is a better way of doing it.