Question

Use the Change of Base Formula to evaluate log4 56. Then convert log4 56 to a logarithm in base 5. Round to the nearest thousandth.

a. 1.748; log5 70

b. 4.025; log5 107.049

c. 2.904; log5 70

d. 2.904; log5 107.049

Answer 1

Hi ,

In order to evaluate a non- standard base log , we have to use the Change of the base formula:

Change of the base formula:
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log b ( a ) = [ log x ( a )/ log x ( b ) ]

According to our problem ,

log 4 ( 56 ) = [ log 5 ( 56 )/ log 5 ( 4 ) ]

Using the natural log as our new base log :

log 4 ( 56 ) = [ log ( 56 )/ log ( 4 ) ]

= 2.90367746

= 2.904 ( Round to the nearest thousandth )

Option C is correct.

Hope this will helps you.