Chapter 10: Q. 10.76 (page 1048)

Solve: $3 \log x = \log 64$

Short Answer

Expert verified

By solving the expression, $3 \log x = \log 64$ , the value of $x$ is $4$

Step by step solution

Step 1. Given

An expression $3 \log x = \log 64$

To solve the expression

Step 2. Use the Power Property of logarithm.

Use the Power Property.

$3 \log x = \log 64$

$\log x^{3} = \log 64$

Step 3. Use the One-to-One Property

Use the One-to-One Property, if $\log_{a} M = \log_{a} N$ , then $M = N$

$x^{3} = 64$

Step 4. Solve using the Square Root Property.

Solve using the cube Root Property.

$x^{3} = 64 4^{3} = 64$

So the value of $x$ is $4$

Step 5. To check the solution

Substitute $x = 4$ in the original equation.

$3 \log (4) = \log 64 \log {(4)}^{3} = \log 64 \log 64 = \log 64$

Hence the solution has been checked.

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Solve: $3 \log x = \log 64$

Short Answer

Step by step solution

Step 1. Given

Step 2. Use the Power Property of logarithm.

Step 3. Use the One-to-One Property

Step 4. Solve using the Square Root Property.

Step 5. To check the solution

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Solve: 3logx=log64

Short Answer

Step by step solution

Step 1. Given

Step 2. Use the Power Property of logarithm.

Step 3. Use the One-to-One Property

Step 4. Solve using the Square Root Property.

Step 5. To check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Calculus

Geometry

Decision Maths

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve: $3 \log x = \log 64$