Chapter 10: Q. 95 (page 1018)

In the following exercises, solve each equation:
$2^{3 x - 8} = 16$

Short Answer

Expert verified

The solution of the given equation is $4 .$

Step by step solution

Step 1. Given Information

The given equation is $2^{3 x - 8} = 16 .$

We have to solve it.

Step 2. Solve the equation

To solve the equation, write both sides of the equation with the same base.

So, $2^{3 x - 8} = 2^{4}$

Now, write a new equation by setting the exponents equal.

$3 x - 8 = 4 3 x = 4 + 8 3 x = 12 x = 4$

Step 3. Verify the solution

To verify the solution, substitute $x = 4$ in the original equation.

role="math" localid="1644922900843" $2^{3 (4) - 8} = 16 2^{12 - 8} = 16 2^{4} = 16 16 = 16$

Hence, our result is true.

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In the following exercises, solve each equation:
$2^{3 x - 8} = 16$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solve the equation

Step 3. Verify the solution

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In the following exercises, solve each equation:23x-8=16

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solve the equation

Step 3. Verify the solution

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, solve each equation:
$2^{3 x - 8} = 16$