Chapter 10: Q. 432 (page 1065)

In the following exercises, solve for x.
$3 \log_{5} x = \log_{5} 216$

Short Answer

Expert verified

The value ofxfor the equation $3 \log_{5} x = \log_{5} 216$ is $6$

Step by step solution

Step 1. Given data

The given Logarithmic Equation is $3 \log_{5} x = \log_{5} 216$

Step 2. Apply the power properties of the logarithm

Use power properties of the logarithm $\log_{a} (m^{p}) = p \log_{a} (m)$

$3 \log_{5} x = \log_{5} 216 \log_{5} x^{3} = \log_{5} 216$

Step 3. Apply one to one property of logarithm

Use one to one property of the logarithm, if $\log_{a} (m) = \log_{a} (n)$

then $m = n$

$\log_{5} x^{3} = \log_{5} 216 x^{3} = 216 x = \pm 6$

the logarithm of a negative number is not possible

so $x = 6$

Step 4. verification

Substitute $6$ for $x$ in the equation

localid="1645036653424" $3 \log_{5} x = \log_{5} 216 3 \log_{5} 6 \overset{?}{=} \log_{5} 216 \log_{5} 6^{3} \overset{?}{=} \log_{5} 216 \log_{5} 216 = \log_{5} 216$

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In the following exercises, solve for x.
$3 \log_{5} x = \log_{5} 216$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Apply the power properties of the logarithm

Step 3. Apply one to one property of logarithm

Step 4. verification

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In the following exercises, solve for x.3log5x=log5216

Short Answer

Step by step solution

Step 1. Given data

Step 2. Apply the power properties of the logarithm

Step 3. Apply one to one property of logarithm

Step 4. verification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Logic and Functions

Statistics

Geometry

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve for x.
$3 \log_{5} x = \log_{5} 216$