solve these equations?

Question

1) log4 (m+2) - log4 (m-5) = log4 8
answers: 6,0,2,no real solution

2) log4 z + log4 8 = log4 24
answers: 3,6,2,16

Answer 1

1) log[base 4](m + 2) - log[base 4](m - 5) = log[base 4](8)

Your first step is to use the property that
log[base b](a) - log[base b](c) = log[base b](a/c).
Doing this to the left hand side,

log[base 4]{ (m + 2)/(m - 5) } = log[base 4](8)

Now that we have log[base 4] on both sides, we can equate their insides. This yields

(m + 2)/(m - 5) = 8

Now, we solve as normal. Multiplying both sides by (m - 5)

m + 2 = 8(m - 5)
m + 2 = 8m - 40
42 = 7m; therefore
m = 6.

2) log[base 4](z) + log[base 4](8) = log[base 4](24)

Moving log[base 4](8) to the right hand side,

log[base 4](z) = log[base 4](24) - log[base 4](8)

Now, using the earlier log property,

log[base 4](z) = log[base 4](24/8)
log[base 4](z) = log[base 4](3)

Now, equating the insides of the logs,

z = 3

Answer 2

log4 (m+2) - log4 (m-5) = log4 8
log4 (m+2)/(m-5) =log4 8
without taking the logarithm of both sides
(m+2)/(m-5)=8
8m-40=m+2
7m=42

Answer
m=6

2)
log4 z=log4 24-log4 8
log4 z=log4 24/8
log4 z = log4 3

Answer
z=3

Answer 3

log4 (m+2) - log4 (m-5) = log4 8
log4((m+2)/m-5)) log4 8
(m+2)/(m-5) = 8
m+2 = 8m -40
42 = 7m
m= 6

Answer 4

1) you can solve it as below:
log4 (m+2) - log4 (m-5) = log4 ((m+2)/(m-5))
now you can 'exp' both side of the equation and it becomes:
(m+2)/(m-5)=8
which is equal to:
m+2=8m-40
so:
m=6
------------------------
2) this question solves like above:
log4 z + log4 8=log4 8z
now we exp both side of the equation:
8z=24
so:
z=3
--------------------------
Good Luck...