## anonymous 5 years ago Convert log110 to an expression containing only natural logarithms

1. anonymous

change of base formula says $log_b(x)=\frac{log_a(x)}{log_a(b)}$ but i cannot read exactly what you wrote. your answer will look like $\frac{ln(x)}{ln(10)}$ if your base is ten.

2. anonymous

Thanks, the question is really Log10(110) (10 being th base) So what is the x value on the top of the fraction [ln(x)]?

3. anonymous

ok change of base formula: on top goes log of input, on bottom goes log of base.

4. anonymous

k

5. anonymous

the base here is ten, so you use $log_10(110)=\frac{ln(110)}{ln(10)}$

6. anonymous

this is why fancy calculators only have the natural log. you can always convert. it is also how you solve $b^x=A$ for x

7. anonymous

Thanks alot my good man.

8. anonymous

welcome