Exponential and Logarithmic Functions

Convert

100

10²=100

What is log₁₀100=2?

200

t=log₃8

What is 3^t=8?

300

16^1/4=2

What is log₁₆2=1/4?

400

log₄4=1

What is 4¹=4?

500

4^0.5=2

What is log₄2=0.5?

Solve

100

log₄x=3

What is 64?

200

log₃₂x=1/5

What is 2?

300

4^3x+5=16

What is x=-1?

400

logx+log(x-9)=1

What is x=10?

500

log₄(x+3)+log₄(x-3)=2

What is x=5?

Simplify

100

7^(log₇10)

What is 10?

200

log₈8¹⁰⁰

What is 100?

300

log₄4

What is 1?

400

log₃1

What is 0?

500

Express as a single logarithm and simplify: 1/2log_ax+3log_ay-2log_ax

What is log_a(x^1/2y³)/x²?

Express

100

Express as a sum: log₃(27*81)

What is log₃27+log₃81?

200

Express as a difference: log_b(62/12)

What is log_b62-log_b12?

300

Express as a product: log_ax³

What is 3log_ax?

400

Express as a single logarithm: 2/3log_ax+1/2log_ay

What is log_a(x^2/3*sqrty)

500

e^x=3, what is x????

What is ln3

Find

100

Given log₁₀2=0.301 and log₁₀3=0.477, what is log₁₀6?

What is 0.778?

200

Given log_a3=0.43, find log_a27.

What is 3*0.43?

300

Given log_a4=0.67 and log_a3=0.2, find log_a(4/3):

What is 0.47?

400

Given log_ax=0.87 and log_ay=0.3, find log(xy³)

What is 1.77?

500

lnx=4

What is x=e⁴