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17-07-2014
Mathematics

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Log4 8= simplify using properties of logarithm

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17-07-2014

8 = (2) cubed.

So log(8) in any base = 3 log(2) in the same base.

But 2 is the square root of 4, so in the base of 4, log₄(2) = 1/2

log₄(8) = 3 log₄(2) = 3 x 1/2 = 1.5

Answer Link

17-07-2014

using logarithm property,
log4(8) = log10(8) / log10(4)
= log10(2)^3 / log10(2)^2
= 3*log10(2) / 2*log10(2)
= 3/2
= 1.5

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