Chapter 10: Q. 10.27 (page 1014)

Solve:
$3^{3 x - 2} = 81$

Short Answer

Expert verified

By solving the equation $3^{3 x - 2} = 81$ , the value of $x$ is $2$

Step by step solution

Step 1. Given

An expression $3^{3 x - 2} = 81$

To solve the expression.

Step 2. Write both sides of the equation with the same base.

Since the left side has base $3$ , write the right side with base $3$ .

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

$3^{3 x - 2} = 3^{4}$

Step 3. Write a new equation by setting the exponents equal.

Since the bases are same, the exponents must be equal.

$3 x - 2 = 4$

Step 4. Solve the equation

Solve the equation

$3 x - 2 = 4 3 x = 4 + 2 3 x = 6$

Divide both sides by $3$ ,

$x = 2$

Step 5. Check the solution.

Substitute $x = 2$ in the original equation and solve.

$3^{3 x - 2} = 81 3^{3 (2) - 2} = 81 3^{6 - 2} = 81 3^{4} = 81$

Hence the equation has been checked.

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Solve:
$3^{3 x - 2} = 81$

Short Answer

Step by step solution

Step 1. Given

Step 2. Write both sides of the equation with the same base.

Step 3. Write a new equation by setting the exponents equal.

Step 4. Solve the equation

Step 5. Check the solution.

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Solve:33x-2=81

Short Answer

Step by step solution

Step 1. Given

Step 2. Write both sides of the equation with the same base.

Step 3. Write a new equation by setting the exponents equal.

Step 4. Solve the equation

Step 5. Check the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Theoretical and Mathematical Physics

Statistics

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Solve:
$3^{3 x - 2} = 81$