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log8(5) = b. Express log4(10) in terms of b

log85=b

using the base change rule

log85=log45/log48

log48 can be solved:

log48=x

4x=8

22x=23

2x=3

x=3/2

Therefore we can write:

log85=log45/(3/2)=b

 log45=(3/2)b                [1]

To make  log45 into log410 we can use the product rule:

log42+log45=log4(2x5)=log410

So by adding log42 on both sides of equation [1] we can write

log42+log45=log42+ (3/2)b 

log410=log42+ (3/2)b 

But log42 can be solved:

log42=x

4x=2

22x=2

2x=1

x=1/2

Therefore we can conclude that

log410=1/2+ (3/2)b 

log410=(1+3b)/2 

Answered by Beatrice M. Maths tutor

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