Question

Evaluating base logarithms?

Answer 1

Hint:
it is better if you change the base of logarithm, from 5 to 10. So, for example, the first logarithm is equal to:
\[\Large {\log _5}80 = \frac{{{{\log }_{10}}80}}{{{{\log }_{10}}5}}\]

Answer 2

use the change of base formula on

log_48 (3)

to get

log_48 (3) = log(48) / log(3)


and then, I think you are expected to evaluate this with your calculator
ie enter `( log ( 48 ) ) / ( log ( 3 ) ) =`

this should match with the first part of some of the options

Answer 3

this should equal `some.number`

so you have

x = log_48 (3) = `some.number`


Converting this to have a base of 5

x = log_5 ( 5 ^ `some.number` )

then evaluate 5 ^ `some.number`


x = log_5 ( `another.number` )

Answer 4

and the right option will be of the form

`some.number`; log_5 ( `another.number` )

Answer 5

@JoeJoldin
Does it make any sense?