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Question
If log 4 = 0.6020, find the value of each of the following: log8
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Solution
To find the value of log 8 given log 4 = 0.6020, we can use the properties of logarithms.
8 = 4 × 2
4 = 22
`2 = 4^(1/2)`
`8 = 2^3`
`= (4^(1/2))^3`
`= 4^(3/2)`
Using the power rule of logarithms, log(xn) = n log x
`log 8 = log(4^(3/2))`
`log8 = 3/2 * log4`
log 8 = 1.5 × 0.6020
log 8 = 0.9030
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