SOLUTION: Log problems I am stuck on: {{{ log(((0.01x^3)/(x^2+4x+4)))^5 }}} I must write so that it does not contain products, quotients or powers What I got: {{{ (1/5) 3log(0.01x

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Log problems I am stuck on: {{{ log(((0.01x^3)/(x^2+4x+4)))^5 }}} I must write so that it does not contain products, quotients or powers What I got: {{{ (1/5) 3log(0.01x      Log On


   

Question 933477: Log problems I am stuck on:

+log%28%28%280.01x%5E3%29%2F%28x%5E2%2B4x%2B4%29%29%29%5E5+
I must write so that it does not contain products, quotients or powers
What I got: +%281%2F5%29+3log%280.01x%29-2log%28x%29-log%284x%29-log%284%29+
Idk if is right or wrong

The other problem is:

+log%28%28base3%29%29+root%283%2C81%29%2Be%5E%28-4ln%28t%29%29+

I must write it without logs and negative exponent
Not sure how to go about that one
Please help
Thank you
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Your first one is badly written. You might be starting with this:
log((((0.01x^3)/(x^2+4x+4))*5)), if pure text form, or when rendered (which may fail in appearance here),
log%28%28%28%280.01x%5E3%29%2F%28x%5E2%2B4x%2B4%29%29%2A5%29%29.

A good possible first step is
log%28%280.01x%5E3%29%29%2Blog%28%285%29%29-log%28%28x%5E2%2B4x%2B4%29%29

log%28%280.01%29%29%2Blog%28%28x%5E3%29%29%2Blog%28%285%29%29-log%28%28x%5E2%2B4x%2B4%29%29

-2%2B3%2Alog%28%28x%29%29%2Blog%28%285%29%29-log%28%28%28x%2B2%29%5E2%29%29

highlight%28-2%2B3%2Alog%28%28x%29%29%2Blog%28%285%29%29-2%2Alog%28%28x%2B2%29%29%29 which you can arrange in other equivalent ways based on commutative property of addition.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28%28%280.01x%5E3%29%2F%28x%5E2%2B4x%2B4%29%29%29%5E5+

+%281%2F5%29log%28%28%280.01x%5E3%29%2F%28x%5E2%2B4x%2B4%29%29%29+

+%281%2F5%29%28log%28%280.01x%5E3%29%29-log%28%28x%2B2%29%5E2%29%29%29+

+%281%2F5%29%283log%28%280.01x%29-2log%28%28x%2B2%29%29%29%29+



+log%283%2Croot%283%2C81%29%29%2Be%5E%28-4ln%28t%29%29+

+log%283%2Croot%283%2C3%5E3%29%29%2Be%5E%28-4ln%28t%29%29+
+log%283%2C3%2Be%5E%28-4ln%28t%29%29%29+........e%5E%28-4ln%28t%29%29=1%2Fe%5E%28ln%28t%5E4%29%29=1%2Ft%5E4
+log%283%2C3%2B1%2Ft%5E4%29+
+log%283%2C%283t%5E4%2B1%29%2Ft%5E4%29%29+
+log%283%2C%283t%5E4%2B1%29%2Ft%5E4%29%29+...in base 10
+log%28%283+t%5E4%2B1%29%2Ft%5E4%29%29%2Flog%283%29+

+t+=+-%28-1%2F2%29%5E%281%2F4%29+........t = -(-1/2)^(1/4)
t+=+%28-1%2F2%29%5E%281%2F4%29....t = (-1/2)^(1/4)
t+=+-%28-1%29%5E%283%2F4%29%2A2%5E%28-1%2F4%29....t = -(-1)^(3/4)/2^(1/4)
t+=+%28-1%29%5E%283%2F4%29%2A2%5E%28-1%2F4%29........t = (-1)^(3/4)/2^(1/4)