What are the steps to solving an exponential function?

Solving Exponential Equations

1. Step 1: Express both sides in terms of the same base.
2. Step 2: Equate the exponents.
3. Step 3: Solve the resulting equation.
4. Solve.
5. Step 1: Isolate the exponential and then apply the logarithm to both sides.

How do you find an exponential equation?

Find the equation of an exponential function

1. If one of the data points has the form (0,a), then a is the initial value.
2. If neither of the data points have the form (0,a), substitute both points into two equations with the form f ( x ) = a ( b ) x \displaystyle f\left(x\right)=a{\left(b\right)}^{x} f(x)=a(b)x​.

How do you calculate exponential value?

If you’d like to work it out by hand, do the following:

1. Determine the base and the exponent.
2. Write the reciprocal of the base and change the sign of the exponent to positive.
3. Write the reciprocal of the base the same number of times as the exponent.
4. Place a multiplication symbol between each.
5. Multiply and get the result.

How to solve exponential equations?

Isolate the exponential part of the equation. If there are two exponential parts put one on each side of the equation. Take the logarithm of each side of the equation. Solve for the variable. Check your solution graphically. Solve the exponential equations. Round to the hundredths if needed.

How to access variables within an exponent in exponential equations?

We can access variables within an exponent in exponential equations with different bases by using logarithms and the power rule of logarithms to get rid of the base and have just the exponent. How to solve exponential equations using logarithms?

How do you solve for x x?

Now, we need to solve for x x. This is easier than it looks. If we had 7 x = 9 7 x = 9 then we could all solve for x x simply by dividing both sides by 7. It works in exactly the same manner here. Both ln7 and ln9 are just numbers.

How to rewrite each side of an exponential equation with different bases?

When it’s not convenient to rewrite each side of an exponential equation so that it has the same base, you do the following: 1 Take the log (or ln) of both sides 2 Apply power property 3 Solve for the variable