9.5 HW - Common Bases

Front

What is a common base in exponential equations?

Back

A common base is a shared base that allows for the simplification of exponential equations, making it easier to solve for unknowns.

Front

How do you solve an equation with the same base?

Back

If two expressions have the same base, you can set their exponents equal to each other to solve for the unknown.

Front

What is the value of a if 5^(a + 2) = 1/125?

Back

a = -5

Front

What is the solution to the equation 3^3 = (3^2)^(2x + 1)?

Back

x = 1/4

Front

How do you rewrite 8 as a power of 2?

Back

8 can be rewritten as 2^3.

Front

If (-3)^x = (-3)^13, what is the value of x?

Back

x = 13

Front

What is the first step in solving exponential equations?

Back

Identify if the bases can be made the same or if logarithms need to be used.

Front

What is the logarithmic form of an exponential equation?

Back

If b^y = x, then log_b(x) = y.

Front

What is the relationship between exponents and logarithms?

Back

Logarithms are the inverse operations of exponentiation.

Front

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

Back

Rewrite 8 as 2^3, then set the exponents equal: 5x + 7 = 3.