Solve Exponential equations 1

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 the equation 8^(3x+3) = 8^6?

Back

Since the bases are the same, set the exponents equal: 3x + 3 = 6. Solving gives x = 1.

Front

What is the solution to the equation 3^3 = 3^(4x + 2)?

Back

Set the exponents equal: 3 = 4x + 2. Solving gives x = 1/4.

Front

How do you solve the equation 16^(x-3) = 8^(x-3)?

Back

Rewrite both sides with the same base: (2^4)^(x-3) = (2^3)^(x-3). This simplifies to 4(x-3) = 3(x-3). Since x-3 cannot be zero, solve for x = 3.

Front

What is the solution to the equation 8 = 2^(5x+7)?

Back

Rewrite 8 as 2^3: 2^3 = 2^(5x + 7). Set the exponents equal: 3 = 5x + 7. Solving gives x = -4/5.

Front

What is the base of an exponential function?

Back

The base of an exponential function is the constant that is raised to a variable exponent. For example, in the function f(x) = a^x, 'a' is the base.

Front

What is the general form of an exponential equation?

Back

The general form of an exponential equation is y = a * b^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent.

Front

What does it mean to isolate the variable in an exponential equation?

Back

Isolating the variable means rearranging the equation so that the variable is on one side and all other terms are on the other side, allowing for easier solving.

Front

What is the importance of having the same base when solving exponential equations?

Back

Having the same base allows you to set the exponents equal to each other, simplifying the process of solving the equation.

Front

How do you convert an exponential equation to logarithmic form?

Back

An exponential equation a^b = c can be converted to logarithmic form as log_a(c) = b.