SOLUTION: I'm having trouble understanding logarithms to a base that's not 10. For example, a homework question is {{{ log (3, 27t^2) }}}. I'm asked to simplify fully without using a calcula

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I'm having trouble understanding logarithms to a base that's not 10. For example, a homework question is {{{ log (3, 27t^2) }}}. I'm asked to simplify fully without using a calcula      Log On


   

Question 940351: I'm having trouble understanding logarithms to a base that's not 10. For example, a homework question is +log+%283%2C+27t%5E2%29+. I'm asked to simplify fully without using a calculator. I've gone as far as +log+%283%2C+%283%5E3%29t%5E2%29+, but I get stuck there, and I'm not even sure I'm on the right path.
Found 3 solutions by josgarithmetic, lwsshak3, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Your exercise shows base 3.

log+%283%2C+%2827t%5E2%29%29
t%5E2%2Alog%283%2C%2827%29%29
t%5E2%2Alog%283%283%5E3%29%29
highlight%283t%5E2%2Alog%283%2C3%29%29

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
For example, a homework question is +log+%283%2C+27t%5E2%29+. I'm asked to simplify fully without using a calculator.
***
log%283%2C27t%5E2%29%29
log%283%2C%2827%29%29%2B2log%283%2C%28t%29%29
3%2B2log%283%2C%28t%29%29

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
I'm having trouble understanding logarithms to a base that's not 10. For example, a homework question is +log+%283%2C+27t%5E2%29+. I'm asked to simplify fully without using a calculator. I've gone as far as +log+%283%2C+%283%5E3%29t%5E2%29+, but I get stuck there, and I'm not even sure I'm on the right path.


log+%283%2C+27t%5E2%29

log+%283%2C+27%29+%2B+log+%283%2C+t%5E2%29

log+%283%2C+3%5E3%29+%2B+2+%2A+log+%283%2C+t%29

highlight_green%283+%2B+2log+%283%2C+%28t%29%29%29