Question

If log 4 = 0.6020, find the value of each of the following: log8

Answer 1

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