College Algebra & Trigonometry, 2018a

3.4. SOLVING LOGARITHMIC EQUATIONS 175
And, solve for x
100x − 200 = 5x − 1
95x = 199
x = 199
95
In some equations, all of the terms are stated using logartihms. These equations
often come out in a form that says log b x =log b y. If this is the case, we can then
conclude that x = y.
It seems reasonable that if the exponent we raise b to in order to get x is the same
exponent that we raise b to in order to get y, then x and y are the same thing.
Assume:
Example
Solve for x.
log b x =log b y
Let’s say that log b x = a =log b y
then
b a = x and b a = y
if both x and y are equal to b a , then x = y
log 5 (4 − x) =log 5 (x +8)+log 5 (2x + 13)