SOLUTION: the problem is- (1/2) raised to the x and it is equal to 4. first thing i know we have to do is, to set the bases equal, but since this is a fraction, i'm not quite sure on how to

Question 112397This question is from textbook A graphical Approach to College Algebra
: the problem is- (1/2) raised to the x and it is equal to 4. first thing i know we have to do is, to set the bases equal, but since this is a fraction, i'm not quite sure on how to get there. which is what i need help on...is how to find the same base for this problem since it is a fraction! This question is from textbook A graphical Approach to College Algebra

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
Note that is equivalent to
.
This being the case, In the given equation you can replace with and
when you do that the original equation becomes:
.

.
Then applying the power rule of exponents [the rule that says ]
you can reduce the equation by multiplying the two exponents -1 and x to get:
.

.
Now notice that the 4 on the right side is equivalent to . Substitute this for 4
and the equation is then:
.

.
Now the bases are the same so the exponents must be equal. Setting the exponents equal results in:
.

.
Solve for x by multiplying both sides of this equation by -1 to convert it to:
.

.
Hope this makes sense to you and helps you to see your way through the problem. The key to
solving this problem was to recognize that by definition is .
.
RELATED QUESTIONS
Hi there, I have a question pertaining to solving exponential equations with common... (answered by richwmiller)