Chapter 10: Q. 96 (page 1018)

In the following exercises, solve each equation:
$2^{2 x - 3} = 32$

Short Answer

Expert verified

The solution of the given equation is $4 .$

Step by step solution

Step 1. Given Information

The given equation is $2^{2 x - 3} = 32 .$

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, $2^{2 x - 3} = 2^{5} .$

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

$2 x - 3 = 5 2 x = 5 + 3 2 x = 8 x = 4$

Step 3. Verify the solution

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

$2^{2 (4) - 3} = 32 2^{8 - 3} = 32 2^{5} = 32 32 = 32$

Hence, our result is true.

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In the following exercises, solve each equation:
$2^{2 x - 3} = 32$

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:22x-3=32

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Step by step solution

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In the following exercises, solve each equation:
$2^{2 x - 3} = 32$