solving these logorithims?

Question

can anyone help me on these

3^2n ≤ 4^15
and
log4 4^15

Answer 1

3^2n≤ 4^15

log(3)^2n≤ log(4)^15

2n(log3)≤ 15log4

2n≤ (15log4)/(log3)

n≤ (15log4)/(2log3)

n≤ 9.4639...

Next problem:

log4 4^15= 15
It's a property

Answer 2

log4 4^15 = 15, by definition.

3^2n <= 4^15
<=> (2n) log 3 <= 15 log 4
<=> 2n <= 15 log 4 / log 3
<=> n <= (15/2) log 4 / log 3
<=> n <= (15/2) log3 4
(use whichever of the last two lines you prefer)