Exponential equations are equations where the variable is in the exponent. For example, the equation 2^x = 8 is an exponential equation because the variable x is in the exponent.
To solve an exponential equation, you want to get the variable by itself on one side of the equation. This can be tricky because the variable is in the exponent, but there is a trick you can use called taking the logarithm of both sides of the equation.
A logarithm is the opposite of an exponent. So if we take the logarithm of both sides of the equation 2^x = 8, we get:
log(2^x) = log(8)
Using a property of logarithms, we can simplify this to:
x * log(2) = log(8)
Then we can solve for x by dividing both sides by log(2):
x = log(8) / log(2)
Using a calculator, we can simplify this to:
x = 3
So the solution to the exponential equation 2^x = 8 is x = 3.
Remember, whenever you have an exponential equation, you can take the logarithm of both sides to solve for the variable.