Question

Given log_a{5}=m
log_a{9}=n

find the value of:
a) log_a{45}
b) log_a{25}
c) log_a{3}

I didn't get what the question is asking for. Can anyone help me in this question please?

Thanks.

Answer 1

Use the laws of logarithm:
log(xy)=log(x)+log(y)
log(x^2)=2log(x)
log(x/y)=log(x)-log(y)
log(sqrt(x))=(1/2)log(x)

Examples:
Given \(log_7(4)=0.7124, log_7(7)=1\)
\(log_7(28)=log_7(4)+log_7(7)=0.7124+1=1.7124\)
\(log_7(16)=2*log_7(4)=2*.7124=1.4248\)
\(log_7(2)=(1/2)log_7(4)=(1/2)0.7124=0.3562\)

Answer 2

take for example, the (a) part of your exercise.
I will only do the first step using Mathmate's response published 39 minutes ago 31 may of 2016.
On the first example he showed you he pretty much gave away the methodology for rewriting a logarithm as a sum of other, you just begin by rewriting the number as a product and later, rewrite as a sum of logarithms:
\[\log(45)=\log(9 \times 5) = \log(9)+ \log(5) \]

Answer 3

@sweetburger

You might want to rewrite your 'equality'

Answer 4

@Zarkon woops do correct me if im wrong again.

how about like this then
\[\log_{a}9= \log_{a}(3^2)=2\log_{a}3 \]

\[\log_{a}9=2\log_{a}3=n \]

then
\[2\log_{a}3=n, \frac{ n }{ 2 } =\log_{a} 3\]

Answer 5

Thanks for the help everyone. I was so confused with this question and now I know how to do this. Thanks.