Algebra II : Solving Exponential Equations

Example Questions

Example Question #48 : Solving And Graphing Exponential Equations

Solve the equation:

Explanation:

Notice that we can rewrite the right side of the equation as an exponent.

The equation  becomes:

Now that the bases of the exponential term are equal, the powers can be set equal to each other.

Simplify the equation.

Divide by six on both sides.

Example Question #49 : Solving And Graphing Exponential Equations

Solve:

Explanation:

Change the base on the right side to base ten.

Replace the hundred with this term.

Set the powers equal to each other now that the bases are equivalent.

Solve for the x-variable.  Distribute the two on the right side.

Divide by eight on both sides.

Example Question #41 : Solving And Graphing Exponential Equations

Solve:

Explanation:

The bases of the equation are alike, which means we do not need to change the power.  We can simply set the powers equal and solve for the unknown variable.

Divide by 12 on both sides.

Example Question #41 : Solving Exponential Equations

Solve:

Explanation:

Rewrite the right side with a negative exponent.  The goal is to establish similar bases to set the powers equal to each other.

Set the powers equal to each other.

Subtract one from both sides.

Divide by three sides.

Example Question #42 : Solving Exponential Equations

Solve:

Explanation:

Convert all the terms to base ten.

Use distribution to simplify the powers in parentheses.

On the left side, since we are multiplying powers of the same base, we can add the exponents.

Set the powers equal to each other now that the bases are similar.

Subtract  on both sides.

Divide by negative 19 on both sides.

Example Question #43 : Solving Exponential Equations

Solve:

Explanation:

Convert the base of the right side to base four.

With common bases, the powers can be set equal to each other.

Simplify the right side.

Subtract  on both sides.

Divide by negative six on both sides.

Reduce both fractions.

Example Question #44 : Solving Exponential Equations

Solve:

Explanation:

In order to solve this equation, we will need to change the bases of both terms.

Notice that both bases can be four raised to some power.

Replace the terms.

Set the powers equal to each other.

Divide by two on both sides.

Subtract  on both sides.

Divide by seven on both sides.

Example Question #45 : Solving Exponential Equations

Solve for .

Explanation:

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents.

With same base, we can write:

Subtract  on both sides.

Divide  on both sides.

Example Question #46 : Solving Exponential Equations

Solve for .

Explanation:

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents.

With the same base, we can write:

Divide  on both sides.

Example Question #47 : Solving Exponential Equations

Solve:

Explanation:

Rewrite the second term in terms of base two.

Rewrite the equation.

Set the powers equal to each other.

Do NOT divide by x on both sides or we will get no solution!