Log and Exponential Word Problems

Change to Exponential Form:
log₆36 = 2

• 2⁶=36
• 6²=36
• 36²=6
• 36⁶=2

Change to Logarithmic Form:
5³ = 125

• log ₅ 125 = 3
• log ₃ 125 = 5
• log ₅ 3 =125
• log₁₂₅ 3 = 5

Condense to a single logarithm.

• ln x⁴/ y

• ln xy⁴

• ln x/ y⁴

• ln x⁴/ y⁴

Condense.

• log₂x²y¹⁰
• log₂x²+log₂y¹⁰
• log₂x²/y¹⁰
• log₂10xy

Expand.

• log x + 5 log y
• 5 log x + 5 log y
• 5 log x - log y
• log x - 5 log y

Condense

• logxyz³
• log(xy/z³)
• logx+logy+logz³
• logx³y³z³

Expand

• 6log₈v-2log₈u
• 6log₈u-2log₈v
• 3log₈u-2log₈v
• 6log₈u+2log₈v

Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years?

• $1,584.62
• $2,651.39
• $2,706.86
• $1,825.10

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

• $15,415.94
• $15,683.28
• $15,927.56
• $16,109.05

Approximately what interest rate would be needed in order to grow an investment of $1,400 to $2,500 in 10 years if the interest was compound monthly?

• 5.96%
• 5.84%
• 5.81%
• 5.88%