SOLUTION: Solve for x to three significant digits. 3 Superscript 6x Baseline equals 5 Superscript 7x minus 6

I can't tell whether you mean this

 or this 

I'll assume you mean the first way, because the 
second interpretation requires iterative methods
or a graphing calculator.



then since the bases are positive and equal
and not equal to 1, then we can just equate
the exponents:





----------------

But if you mean 



Then it cannot be solved with algebra or logarithms.

If you have a TI-83 or 84,

Press Y=

Make the first two lines read like this:

\Y1=5^(6X)
\Y2=5^(7X)-6

Press ZOOM
Press 6
Press 2ND
Press TRACE
Press 5
Press ENTER
Press ENTER 
Press ENTER

Read at bottom of screen

X=.25553448

Round to three significant digits:

X=0.256

Edwin