How do you use the Change of Base Formula and a calculator to evaluate the logarithm ${log}_{9} 2.15$ $log_9 2.15$ ?

Question

1466 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-16T11:55:45

I found: $0.3483$ $0.3483$

The Change of Base Formula allows you to write:

${log}_{a} b = \frac{{log}_{c} b}{{log}_{c} a}$ $log_ab=(log_cb)/(log_ca)$
and change your base from $a$ $a$ to the new base $c$ $c$ .

We can choose, as new base, $e$ $e$ and use natural logs, $ln$ $ln$ , that can be evaluated using a pocket calculator and get:

${log}_{9} (2.15) = \frac{ln 2.15}{ln 9} = 0.3483$ $log_9(2.15)=(ln2.15)/(ln9)=0.3483$

How do you use the Change of Base Formula and a calculator to evaluate the logarithm log92.15log_9 2.15?