PC_2.3 Solving Exponential Eqs with Common Bases

Front

Define an exponential equation.

Back

An exponential equation is an equation in which a variable appears in the exponent, typically in the form of a^x = b, where a and b are constants.

Front

What is the base in an exponential expression?

Back

The base is the constant number that is raised to a power in an exponential expression, represented as a^x.

Front

How do you solve exponential equations with common bases?

Back

To solve exponential equations with common bases, rewrite both sides of the equation with the same base and then set the exponents equal to each other.

Front

Solve for x: 12^(2x-10) = 1

Back

x = 5

Front

Solve for x: 7^(-x) = 49

Back

x = -2

Front

What is the value of x if 3^(x) = 9?

Back

x = 2

Front

If 2^(x) = 8, what is x?

Back

x = 3

Front

Solve for x: 5^(x+1) = 25

Back

x = 1

Front

What is the relationship between exponents and logarithms?

Back

Logarithms are the inverse operations of exponentiation, allowing us to solve for the exponent in equations of the form a^x = b.

Front

If a^x = a^y, what can we conclude about x and y?

Back

If a^x = a^y, then x = y, provided that a is not equal to 0 or 1.