Laws of Logarithms

1. Use the Laws of Logarithms to evaluate the expression.   solution

(a) $\log(5)+\log(200)$  (b) $\log_6(108)+\log_6(12)$   (c) $\log_3(1161)-\log_3(43)$   (d) $\frac{1}{3}\log_4(64)$

2. Write the following in condensed form.  solution

(a) \(\displaystyle{ \log x + 2 \log y}\)

(b) \(\displaystyle{ 2\ln x - 5\ln(x^2 + 1) }\)

(c) \(\displaystyle{ 2\ln x - \frac{1}{2} \ln(x^2 + 1) }\)

(d) \(\displaystyle{ 3\log_5(3x + 10) - 2\log_5(x^2 - 4x) + 4\log_5(z)}\)

3. Write the following in expanded form. Where possible, evaluate the log expressions.  solution

(a) \(\displaystyle{\ln [x(x+5)]} \)       (b) \(\displaystyle{ \log_2 \frac{x^4}{8} }\)        (c) \(\displaystyle{ \log_7 \frac{\sqrt 7}{x^3} }\)       (d) \(\displaystyle{ \ln \frac{2e^2}{3}}\)