Three Laws of Logarithms

I. Use the properties of logarithms to write the expression
as a sum,difference and/or constant multiple of logarithms.

1. log37x 4.
2. log3(7/x) 5.
3. log3x7 6.


II. Use the properties of logarithms to write the expression

as the logarithm of a single quantity.

7. logax + logay 11. (1/3) loga4x
8. logax - loga(y+1) 12. log x - 2[log(x+2) + log(x-2)]
9. 3 logax + 2logay 13. (1/2)[log(x+1) + 2 log(x-1)] + 2 log x
10. logax + 2loga(y+1) - 3logaz 14.

III. Find exact values without using a calculator.

15. log2 4 2.3 17. 5 ln e3
16. log3 18 - log 3 2 18. log6 3 + log 6 12