solving logarithmic equations

Solve the logarithmic equation. When necessary, round answer to the nearest hundredth. log 4 x/2 = 2

32

Find the value of x in 4000(1.5x) = 25,000. Show your work.

4000(1.5^x)=25000 divide both sides by 4000 1.5^x=6.25 take the natural log of both sides xln(1.5)=ln(6.25) divide both sides by ln(1.5) x=ln(6.25)/ln(1.5) x≈4.52

Use complete sentences to describe how logarithms can aid in difficult calculations.

To do these calculations using logarithms, we used the theorems and definitions of logarithms and the common logarithm table.

Solve the logarithmic equation. When necessary, round answer to the nearest hundredth. log 3(x + 4) - log 3(x + 2) = log 3 27

x ≈ -1.92

Solve the logarithmic equation. When necessary, round answer to the nearest hundredth. 4 - 3 ln x = -8

x ≈ 54.6

Solve the logarithmic equation. When necessary, round answer to the nearest hundredth. log 5 x + log 5(2x + 3) = 1

x=1

Solve the logarithmic equation. When necessary, round answer to the nearest hundredth. log x 36 = 2

x=6