Calculate without using tables or calculators log 450 and log 324 given log 2 =0.3010 and log 3 =0.4771

Answer 1

I will do the second one
324 = 4(81)
= 2^2 x 3^4

log324 = log(2^2 x 3^4)
= log 2^2 + log 3^4
= 2log2 + 4log3
= 2(.3010) + 4(.4771)
= .6020 + 1.9084
= 2.5104

log(450) = log(10x45)
= log(10x9x5)
= log10 + log 3^2 + log5 ---> need log5

other combinations:
450 = 5^2 x 9x2 = 5^2 x 3^2 x 2 --- still need log 5

Answer 2

log 450= log9 × log50
log3^2 × log 100÷2
Log100=2 So it's 2log3 × log 100÷2
2 (0.4771) × 2 - 0.3010
0.9542 + 1.699
2.6532