SOLUTION: Hi, How do I find the exact value of t given {{{ 7^(2t)= 3^5 }}} I'm not sure how to do this, but I think it has something to do with logs. Thanks.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hi, How do I find the exact value of t given {{{ 7^(2t)= 3^5 }}} I'm not sure how to do this, but I think it has something to do with logs. Thanks.      Log On


   

Question 879048: Hi, How do I find the exact value of t given +7%5E%282t%29=+3%5E5+
I'm not sure how to do this, but I think it has something to do with logs.
Thanks.
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
+7%5E%282t%29=+3%5E5+
+49%5Et+=+243+
t*log(49) = log(243)
t = log(243)/log(49)

Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Base Ten Logarithms,

log%2810%2C7%5E%282t%29%29=log%2810%2C3%5E5%29
2t%2Alog%2810%2C7%29=5%2Alog%2810%2C3%29
highlight%28t=%285%2F2%29%28log%2810%2C3%29%2Flog%2810%2C7%29%29%29




log%2810%2C5%29=0.69897
log%2810%2C7%29=0.845098