SOLUTION: Here is my question: 7^logx = 7 the answer is 10, but I am not quite sure what to do when the log is an exponent of 7. I'm also supposed to show a check of my answer. Than

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Here is my question: 7^logx = 7 the answer is 10, but I am not quite sure what to do when the log is an exponent of 7. I'm also supposed to show a check of my answer. Than      Log On


   



Question 20616: Here is my question:
7^logx = 7
the answer is 10, but I am not quite sure what to do when the log is an exponent of 7. I'm also supposed to show a check of my answer.
Thanks
Sandy

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Recall this about logarithms:
If a%5Ex+=+a%5Ey, the bases are the same, that is a = a, then the exponents are equal, therefore x = y. Applying this to your problem:
7%5E%28logx%29+=+7%5E1 The bases are the same so the exponents are equal.
log%28x%29+=+1 Change to exponential form.
Recall that log(x) is log to the base 10 of x:
Logarithmic form: y = log(x)...Exponential form: x = 10^y
x+=+10%5E1
So, x = 10
Check:
7%5E%28logx%29+=+7
7%5Elog10+=+7 but log10 = 1
7%5E1+=+7