Properties of Logarithms

Write the expression as a single logarithm.   Then simplify if possible.
log₅3 + log₅6 + log₅9

• log₅69
• log₅56
• log₅162
• log₅98

Write the expression as a single logarithm.   Then simplify if possible.
log 6 - log 3 + 2 log 7

• log 98
• log 78
• log 56
• log 45

• log₅(x²z²y¹⁰)
• log₅(z²y²x¹⁰)
• log(zy²x¹⁰)
• log₅(z² + y² + x¹⁰)

• log(x) + log(z) + 4log(y)
• 3log(x) − log(z) − 4log(y)
• 3log(x) + log(z) + 4log(y)
• log(x) − 4log(z) − 3log(y)

Simplify:  $\log_4\left(x+4\right)-\log_4\left(x-5\right)$  

•  $\log_49$  

•  $\log_4\left(2x-1\right)$  

•  $\log_4\left(x^2-x-20\right)$  

•  $\log_4\left(\frac{x+4}{x-5}\right)$  

Simplify:  $2\log_3\left(11x\right)$  

•  $\log_3\left(22x\right)$  

•  $\log_3\left(121x\right)$  

•  $\log_3\left(121x^2\right)$  

•  $\log_3\left(11x^2\right)$  

Simplify:  $\frac{1}{4}\log_516+3\log_5x$  

•  $\log_5\left(4x^3\right)$  

•  $\log_5\left(2x^3\right)$  

•  $\log_5\left(6x\right)$  

•  $\log_5\left(\frac{2}{x^3}\right)$  

Simplify:  $2\log_2x-\log_2\left(x+3\right)$  

•  $\log_2\left(x^3+3x^2\right)$  

•  $\log_2\left(2x^2+6x\right)$  

•  $\log_2\left(\frac{x^2}{x+3}\right)$  

•  $\log_2\left(\frac{2x}{x+3}\right)$  

Simplify:  $\frac{1}{4}\log_281+\frac{1}{2}\log_249$  

•  $\log_221$  

•  $\log_210$  

•  $\log_2\left(\frac{3}{7}\right)$  

•  $\log_244.75$  

Expand.

• $\frac{1}{3}\log x+\log y+\log z$

• $\frac{1}{3}\log x+\frac{1}{3}\log y\ +\frac{1}{3}\log z$

• $\frac{1}{3}\log x-\frac{1}{3}\log y-\frac{1}{3}\log z$

• $3\log x+3\log y+3\log z$ 3 log x + 3 log y + 3 log z