4.5 Solving Exponential Equations

Front

What is an exponential equation?

Back

An equation in which a variable appears in the exponent, such as a^x = b.

Front

How do you solve exponential equations with the same base?

Back

Set the exponents equal to each other and solve for the variable.

Front

What is the first step in solving 3^3 = 3^(4x + 2)?

Back

Since the bases are the same, set the exponents equal: 3 = 4x + 2.

Front

What is the solution to the equation 3^(2x) = 27?

Back

x = 3/2, because 27 can be rewritten as 3^3.

Front

How can you express 64 as a power of 4?

Back

64 can be expressed as 4^3.

Front

What is the value of x in the equation 36 = 6^x?

Back

x = 2, because 36 can be rewritten as 6^2.

Front

What is the logarithmic form of the equation 2^x = 8?

Back

x = log_2(8).

Front

How do you rewrite 4^(p+2) = 64 in terms of base 4?

Back

64 can be rewritten as 4^3, so p + 2 = 3.

Front

What is the solution to the equation 4^(p+2) = 64?

Back

p = 1.

Front

What is the relationship between exponential and logarithmic functions?

Back

Logarithmic functions are the inverses of exponential functions.