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Chapter 10: Q. 10.76 (page 1048)

Solve: 3logx=log64

Short Answer

Expert verified

By solving the expression, 3logx=log64, the value of x is 4

Step by step solution

01

Step 1. Given

An expression 3logx=log64

To solve the expression

02

Step 2. Use the Power Property of logarithm.

Use the Power Property.

3logx=log64

logx3=log64

03

Step 3. Use the One-to-One Property

Use the One-to-One Property, if logaM=logaN, then M=N

x3=64

04

Step 4. Solve using the Square Root Property.

Solve using the cube Root Property.

x3=6443=64

So the value of xis 4

05

Step 5. To check the solution

Substitute x=4in the original equation.

3log(4)=log64log(4)3=log64log64=log64

Hence the solution has been checked.

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