Logarithmic Properties and Change of Base

Find the solution to the equation 3^x = 81 using logarithms.

• x = 2

• x = 6

• x = 4

• x = 10

Determine the value of x in the equation 5^x = 125 using logarithms.

• 3

• 4

• 2

• 6

Using the properties of logarithms, solve the problem: log(x) + log(x + 2) = 3, find the value of x.

• x = 7

• x = 10

• x = 12

• x = 5

Use the change of base rule to rewrite this problem:

log₅75

• log(75)/log(5)

• log(5)/log(75)

Condense the following logarithm: 3 log₂ x + 2 log₂ y – 4 log₂ z 

• log₂ x³y²∕z⁴

• log₂ x³y²z⁴

• log₂ xyz⁹

• 9log₂ xyz

Expand the log

log(x⁷)

• log(7x)

• log7+logx

• xlog7

• 7logx

Expand the log: log(3x)²

• 2log(3+x)

• 2log3+logx

• log3+2logx

• 2(log3+logx)

Use the Change of Base Formula to evaluate the expression. \log_927

• 3