Log10^2=0.3010and log10^3=0.4771 evaluate log10^45
assuming base 10, with your unusual notation
(most would write log10(2) or log_10(2) since 10^2 = 10 to the second power)
log45 = log9 + log5 = 2log3 + log5 = 2log + log(10/2)
= 2log3 + log10 - log2
= 2*.4771 + 1 - 0.3010
= 1.6532
makes no sense.
log 10^2 = log 100 = 2 , not .3010
(if no base is shown, the base of the log expression is 10 by default)
If your question means:
log(base10) ( 2 ) = 0.30103
log(base10) ( 3 ) = 0.4771
evaluate log(base10) ( 4.5 )
then
4.5 = 9 / 2 = 3^2 / 2
log(base10) ( 4.5 ) =
2 • log(base10) ( 3 ) - log(base10) ( 2 ) =
2 • 0.4771 - 0.30103 = 0.65317
To evaluate log10^45, we can use the logarithmic property log(a^b) = b * log(a). So, we have:
log10^45 = 45 * log10
Since log10 is a constant value, we need to know its value in order to evaluate log10^45. The value of log10 is approximately equal to 1.
Therefore, log10^45 ≈ 45 * 1 = 45