NTIw5 Solving Exponential Equations (without Logs) HW

Front

What is an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent. For example, in the equation 2^x = 8, x is the variable in the exponent.

Front

How do you solve exponential equations with the same base?

Back

To solve exponential equations with the same base, set the exponents equal to each other. For example, if (-3)^x = (-3)^13, then x = 13.

Front

What is the value of x in the equation (-3)^x = (-3)^13?

Back

x = 13.

Front

How do you express 1/125 as a power of 5?

Back

1/125 can be expressed as 5^(-3) because 125 = 5^3.

Front

What is the solution for a in the equation 5^(a + 2) = 1/125?

Back

a = -5.

Front

How do you solve the equation 4^(3b - 3) = 1/16?

Back

Rewrite 1/16 as 4^(-2) and set the exponents equal: 3b - 3 = -2.

Front

What is the value of b in the equation 4^(3b - 3) = 1/16?

Back

b = 1/3.

Front

How do you solve the equation 2^x = 4^(x + 1)?

Back

Rewrite 4 as 2^2, so the equation becomes 2^x = (2^2)^(x + 1) = 2^(2x + 2). Set the exponents equal: x = 2x + 2.

Front

What is the solution for x in the equation 2^x = 4^(x + 1)?

Back

x = -2.

Front

What is the value of m in the equation 2^(-m) = 2^(3m - 3)?

Back

m = 3/4.