help logarithmic expressions?

Question

can someone show me how to do this

log7 [log3 (log2 8)] =0

and
log5 (4x-1)=log5 (3x+2)

and
evaluating this

log4 4^15

thanks step by step would be awesome

Answer 1

log7 [log3 (log2 8)]
= log7 [log3 (log2 2^3)]
= log7 [log3 3]
= log7 1
= 0.

log5 (4x-1) = log5 (3x+2)
<=> 5^(log5 (4x-1)) = 5^(log5 (3x+2))
<=> 4x-1 = 3x+2
<=> x = 3

log4 4^15
= 15 by definition.

Remember, the definition of logs is:
log[a] b = c <=> a^c = b
or equivalently
log[a] a^b = b
where [a] indicates logs to base a.

Answer 2

first line simply not true
cancel log5 both sides 4x-1=3x+2
x=3
is that log(44)^15? if it is, it is equal to 15*log44 and you can look up log 44 and multiply.