Math Help - Logarithm issues.

1. Logarithm issues.

I have a question that asks me to find the value of the expression $(.65)^5$ in logarithmic form.

Am I correct in assuming that I should be looking the logarithm that is five times greater than that of .65?

$\log (.68)^5=5\log(.68)=5\log (6.8*10^-1)$Therefore the answer is $5*.8129$ or $4.0645+(-1)=3.0645$ ?

2. Originally Posted by MathBlaster47
I have a question that asks me to find the value of the expression $(.65)^5$ in logarithmic form.

Am I correct in assuming that I should be looking the logarithm that is five times greater than that of .65? e^(i*pi) : Yep, due to the power law

$\log (.68)^5=5\log(.68)=5\log (6.8*10^-1)$ e^(i*pi): Indeed

Therefore the answer is $5*.8129$ or $4.0645+(-1)=3.0645$ ? e^(i*pi) : No, you've made a decimal approximation and the question doesn't ask for this
$\log (.68)^5=5\log(.68)=5\log (6.8 \cdot 10^{-1}) = 5\log (6.8) - 1$

I think I should have been a little more careful how I phrased my question, the question asks me to use a table of logarithms to derive my answer, I just wanted to do my due diligence and try to do the working myself.

Follow up question: Is my decimal approximation satisfactory as an answer, given that I was asked to use a table?

4. Originally Posted by MathBlaster47
I think I should have been a little more careful how I phrased my question, the question asks me to use a table of logarithms to derive my answer, I just wanted to do my due diligence and try to do the working myself.

Follow up question: Is my decimal approximation satisfactory as an answer, given that I was asked to use a table?
Hi Mathblaster47,

you made one error, apart from writing 0.68 instead of 0.65 ...

$5[log(6.5X10^{-1})]=5[log(6.5)+log\left(10^{-1}\right)]=5[log(6.5)-1]=5log(6.5)+5(-1)$

5. Originally Posted by Archie Meade
Hi Mathblaster47,

you made one error, apart from writing 0.68 instead of 0.65 ...

$5[log(6.5X10^{-1})]=5[log(6.5)+log\left(10^{-1}\right)]=5[log(6.5)-1]=5log(6.5)+5(-1)$
Hmmm....gotta stop typing so fast....Silly typos!

Ok, so the final answer is $5(.8129)+5(-1)=4.0645+(-5)$?

6. Yes Mathblaster47,

$(0.65)^5=10^{answer}$
$5log(0.65)=(answer)[log(10)]$