Solving Exponential Equations

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 exponent.

Front

How do you solve the equation 2^(x+6) = 32?

Back

Convert 32 to a power of 2: 32 = 2^5. Therefore, x + 6 = 5, leading to x = -1.

Front

What is the base of an exponential function?

Back

The base of an exponential function is the constant that is raised to a power. In the function f(x) = a^x, 'a' is the base.

Front

How do you rewrite 100000 as a power of 10?

Back

100000 can be rewritten as 10^5.

Front

What is the solution to the equation 10^(2x+4) = 100000?

Back

x = 1/2.

Front

What is the property of exponents that states a^m * a^n = a^(m+n)?

Back

This is known as the Product of Powers Property.

Front

How do you solve the equation 5^(-3x - 1) = 25?

Back

Rewrite 25 as 5^2. Therefore, -3x - 1 = 2, leading to x = -1.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^y = x, then log_b(x) = y.

Front

How do you solve the equation 8 = 2^(5x+7)?

Back

Rewrite 8 as 2^3. Therefore, 3 = 5x + 7, leading to x = -4/5.

Front

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

Back

Rewrite 64 as 4^3. Therefore, p + 2 = 3, leading to p = 1.