Laws of Logarithms Expand each logarithm. Use the logarithmic rules to expand logarithms similar to: log M ⋅ N = log M + log n 1. log M 3 ⋅ N 4 M
N3
5
⎛M⎞
3. log ⎜ ⎟ ⎝N⎠
2. log
M5 ⋅N3
P
4. log
Express each of the following as a single logarithm. 5. 3log P + logQ 1
6. log X + logY 2
2
1
7.
log X − logY 3
2
8. 4 log x + 3log x − 2 log x Solve for x: 9. log 2 7x = log 2 x 2 + 12 (
)
(
)
10. log 5 3x 2 − 1 = log 5 2x 11. 2 log b x = log b ( 2x + 3) (
)
12. log b x 2 − 2 + 2 log b 6 = log b ( 6x ) 13. log 5 2 + 2 log 5 x = log 5 ( 3 − x ) 14. log 6 ( x + 1) + log 6 x = 1