SOLUTION: Goodmorning everyone, can some one help me to evaluate this expression; log(subscript 8)8^9??? Thanks Ya'll!

Algebra ->  Expressions -> SOLUTION: Goodmorning everyone, can some one help me to evaluate this expression; log(subscript 8)8^9??? Thanks Ya'll!      Log On


   

Question 105566This question is from textbook Intermediate Algebra
: Goodmorning everyone, can some one help me to evaluate this expression;
log(subscript 8)8^9???
Thanks Ya'll! This question is from textbook Intermediate Algebra

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
log%288%2C8%5E9%29+=+y
.
Note that if you solve for y, the answer is equal to log%288%2C8%5E9%29
.
One way to solve this equation is to translate it to the exponential form of the logarithm.
The translation uses the relationship that:
.
log%28b%2CA%29=+y is equivalent to the exponential form b%5Ey+=+A
.
By comparing the log form in the translation to the log form you were given in this problem
you can see that:
.
b+=+8
A+=+8%5E9 and
y+=+y
.
Substituting the values on the right side for b, A, and y in the exponential form you
get:
.
8%5Ey+=+8%5E9
.
Looking at this equation, you can see that to make the left side equal to the right side
the exponents have to be equal. In other words, y has to be 9 for the two sides to be
equal. And since y is equal to log%288%2C8%5E9%29, then you can say that log%288%2C8%5E9%29 equals 9.
.
Hope this helps you to understand the problem.
.