Question

log(base2)3 * log(base3)4 +3^log(base3)5 = ?

Help me pls

Answer 1

1) (log₂3)(log₃4) = log₂4

[By law of logarithms, {log(base a)b}*{log(base b)c} = log(base a)c]

2) This further simplifies to 2log₂2 = 2 x 1 = 2

[Since 4 = 2^2; log₂4 = log₂(2^2) = 2log2 = 2 x 1 = 2]

3) 3^{log(base3)5} = 5 [BY another law of log, a^{log (base a) b} = b]

4) Thus, log(base2)3 * log(base3)4 +3^log(base3)5 = 2 + 5 = 7