SOLUTION: pls can you help me check my answer.... log(little8)2 i came up with my answer 1/3 am i right

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: pls can you help me check my answer.... log(little8)2 i came up with my answer 1/3 am i right      Log On


   



Question 95607: pls can you help me check my answer....
log(little8)2 i came up with my answer 1/3
am i right

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
You are correct.
.
You were given:
.
log%288%2C2%29+=+y
.
And you can solve this by converting this problem to the exponential form:
.
8%5Ey+=+2
.
Then you can replace 8 by its equivalent form 8+=+2%5E3 and you can note that on the
right side that 2+=+2%5E1. With these changes the exponential form becomes:
.
%282%5E3%29%5Ey+=+2%5E1
.
Now by the power rule of exponents you can multiply the exponents on the left side to get:
.
2%5E%283y%29+=+2%5E1
.
Since the base on both sides is equal to 2, for both sides to be equal the exponents
must be equal. So you can say
.
3y+=+1
.
and solve for y by dividing both sides by 3 to get:
.
+y+=+1%2F3
.
But from up above we said that log%288%2C2%29+=+y so you can substitute 1%2F3 for y
and see that the answer is:
.
log%288%2C2%29+=+1%2F3
.
which is the answer you got, so you did it correctly.
.
Good job! Keep up the good work!!!
.