Can someone explain how to figure out these types of problems?

Question

Solve log3 (x - 4) > 2.

Evaluate log7 49.

If log5 4 ≈ .8614 and log5 9 ≈ 1.3652 find the approximate value of log5 36.

Solve the equation, log4 (m + 2) - log4 (m -5) = log4 8.

Solve, 2^x = 15.

Reiny · Answer

You must know the meaning of logs
Memorize this equivalence and the following example:
log_a x = y <-----> a^u = x
log₂ 8 = 3 <-----> 2^3 = 8

so consider log3 (x - 4) = 2
---> 3^2 = x-4
13 = x

so clearly if log3 (x - 4) > 2
x-4 > 3^2
x > 13

check: let x = 31
log₃(31-4) > 2
log₃ 27 > 2
is 3^3 > 2 ? YES

using the definition of logs I just gave you, you should be able to evaluate log₇ 49

log5 36 = log5 (9 * 4) = log5 9 + log5 4
you are given both of them, so just add the given logs

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

2^x = 15
take log₁₀ of both sides
then
log 2^x = log 15
x log2 = log15
x = log15/log2
= .... , use your calculator