Solving Log Equations
Variable in the exponent
one exponent
Make the bases
the same
Can’t make the
bases the same
8x  2
5  2  7 x 2
23x  2
3x  1
x 
1
3
two exponents
Base:
Exp:
Value:
Solve for x
5
 7 x 2
2
5
log7    x  2
2
5
log7    2  x
2
Make the bases
the same
Can’t make the
bases the same
5x 3  62x
4x 3  82x 1
2
2x 6
2
6 x 3
2x  6  6x  3
9  4x
9
x
4
log5
x 3
Take the log of both sides
 log6
2x
 x  3log5  2x log6
x log5  3log5  2x log6
Move exp in front
Distribute when needed
3log5  2x log6  x log5
3log5  x 2log6  log5 
3log5
2log6  log5 
x
Get x’s on one side &
numbers on the other
Factor out x
Solve for x