Question

Simplify.
1. (1/log base 3 of 60)+ (1/log base 4 of 60)+ (1/log base 5 of 60)

2. (log base 16 of x)+ ( log base 4 of x) + (log base 2 of x)=7

Answer 1

1/log_a(b) = log_b(a), so what you have is

log_60(3) + log_60(4) + log_60(5)
= log_60(3*4*5)
= log_60(60)
= 1

since 16=2^4=4^2, you have

log_16(x) + 2log_16(x) + 4log_16(x) = 7
7log_16(x) = 7
log_16(x) = 1
x=16

Answer 2

-3 · -u · -7v + 8v - 6uv