Exponentials and Logs

Properties of functions

100

The domain of any exponential function y=ab^x is this.

What is all real numbers.

200

The range of an exponential function y=ab^x is dependent on this.

What is the sign of a?

300

In the equation y=ab^x, this must be true of b.

What is 0<b<1 or b>1.

400

The domain of any logarithmic function y=log_b(x) is this.

What is x>0?

500

This line is an asymptote to the graph of y=ab^x.

What is y=0?

Simplify the expression

100

x²x³ simplifies to this.

What is x⁵?

200

x⁹/x⁴ simplifies to this.

What is x⁵?

300

(4x³)² simplifies to this.

What is 16x⁶?

400

This is the reason 2^x+3=8(2)^x.

What is 2^x+3=2^x2³=2³2^x=8(2)^x?

500

This is the reason (1/2)^x=2^-x.

What is (1/2)^x=1^x/2^x=1/2^x=2^-x?

Solve the equation

100

This is the solution set to 3^x=81.

What is x=4?

200

This is the solution set to 3^{x^2}=81.

What is x=-2,2?

300

This is the solution set to 8^2x+3=4^x-4.

What is x=-17/4?

400

This is the solution set to log₃(x)=2.

What is x=9?

500

This is the solution set to ln(x-1)=3.

What is x=e³+1?

Evaluate the logarithm

100

This is the value of log₂(32).

What is 5?

200

This is the value of ln(e³).

What is 3?

300

This is the value of log(1000³).

What is 9?

400

This is the value of (log₄1)(log₅125).

What is 0?

500

This is the value of log₁₆(8).

What is 3/4?

Find an equation

100

This is an equation of the line through the points (0,4) and (1,8).

What is y=4x+4?

200

This is an equation of the exponential function through the points (0,4) and (1,8).

What is y=4(2)^x?

300

This function is the inverse of y=6^x.

What is y=log₆x?

400

This is an equation that describes 3% continuous growth from a starting value of 150.

What is y=150e^0.03t?

500

This function is the inverse of y=log(x+3).

What is y=10^x-3?