Doubt on simplifying logarithms

Question

here's another doubt (sorry I'm a logarithms newbie)

Given: $\log_{10} 2 = a$ and $\log_{10} 3 = b$

Express $\log_{5} 10$ in terms of $a$ and $b$

I don't know from where to start yet. $2$ and $3$ doesn't seems to have much relation with $5$.

Thanks in advance

Answer 1

You don't need $\log_{10}3=b$. Here are some hints.

1. Factor 10 to get a different expression for $\log_510$.
2. Make use of the fact that $\log_ab=1/\log_ba$ to get an expression for $\log_210$ in terms of $a$.
3. Continue in this vein with a bit of algebra.

Answer 2

Hint: what is the relation between $\log_5 10$ and $\log_{10} 5$? Between $\log_{10} 5$ and $\log_{10} 2$?