Laws of Logarithms!

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If M and N are positive numbers and b is a positive number other than 1, then:
1. logbMN= logbM+logbN
2. logbM/N= logbM-logbN
3. logbM= logbN if and only if M=N
4. logbM^K= KlogbM, for any real number K.
** Use property number 4 when trying to solve exponential.

Example 1:
Write the expression in terms of log M and log N.
log (MN)^2
=log2M+log2N

Example 2:
Write the expression in terms of log M and log N.
log cube root of M/N
=1/3logM-1/3logN

Example 3:
Write the expression in terms of log M and log N.
log m^2 square root of N
=2logM+1/2logN

Example 4:
Write the expression as a rational number or as a single logarithm.
log 2 + log 3 + log 4
=log24

Example 5:
Write the expression as a rational number or as a single logarithm.
1/2log69 + log65
=log615

Example 6:
Write the expression as a rational number or as a single logarithm.
2 ln 6 - ln 3
=ln36/ln3
=ln12

Example 7:
Write the expression as a rational number or as a single logarithm.
log A + 2logB -3logC
=logA + logB^2 - logC^3
=log AB^2/C^3