Chapter 10: Q. 98 (page 1018)

In the following exercises, solve each equation:
$3^{x^{2}} = 81$

Short Answer

Expert verified

The solutions of the given equation are $x = 2 a n d x = - 2 .$

Step by step solution

Step 1. Given Information

The given equation is $3^{x^{2}} = 81 .$

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, $3^{x^{2}} = 3^{4} .$

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

$x^{2} = 4 x = \pm \sqrt{4} x = \pm 2$

Step 3. Verify the solution

To verify the solution,

Substitute $x = 2$ in the original equation

role="math" localid="1644924523318" $3^{{(2)}^{2}} = 81 3^{4} = 81 81 = 81$

It is true.

Now, substitute $x = - 2$ in the original equation

$3^{{(- 2)}^{2}} = 81 3^{4} = 81 81 = 81$

It is also true.

Hence, the solutions are $x = 2, - 2 .$

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In the following exercises, solve each equation:
$3^{x^{2}} = 81$

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:3x2=81

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

Recommended explanations on Math Textbooks

Mechanics Maths

Pure Maths

Decision Maths

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each equation:
$3^{x^{2}} = 81$