Question

Use the properties of logarithms to expand the following logarithm.

1. log3 x(x3 + 1)
2. ln⁡〖(x^(-2) z)/y^5 〗
3. log_6⁡〖√a (a-1)〗
4. log(x^3/(yz)^4 )

Answer 1

1. ㏒3 x +㏒3 (x³+1)

2. -2㏑x +㏑z -5㏑y

3. 0.5㏒6 a +㏒6 (a-1)

4. 3㏒x -4(㏒y + ㏒z)

Explanation:

using properties of logarithm

(a) ㏒(mn) = ㏒m + ㏒n

(b) ㏒(m/n) = ㏒m - ㏒n