Question

If log 3 base a=2 and log 8 base b=3,then logged b base a is?

Answer 1

If `log_a3=2 and log_b8=3` then what is `log_ab`?
`a=sqrt(3)` & `b=2` so using a calculator `log_sqrt(3)2=1.262` (4.S.F)

Explanation:

`log_a3=2` (now raise both sides as a power of a)
-> `a^(log_a3)= a^2` (now use exponent of log rule; raising the logarithm of a number as a power of its base gives the number.)
-> `3=a^2` (now take the principal root)
-> `a=sqrt(3)`

Similarly,
`log_b8=3`
-> `8=b^3`
-> `b=2`

Finally,
input `log_sqrt(3)2` into your calculator giving `1.262` (4.S.F)

You can also rewrite the answer using the change of base formula:
`log_yx =log_zx/log_zy`
in our case
`log_sqrt(3)2 =(log_3 2)/log_3sqrt(3)`
-> = `2log_3 2`
Thanks ciumes :)