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Logarithms Practice Test 1

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Question : 16 of 40

Marks: +1, -0

\log_{10} 5 + \log_{10} (5x + 1)

= \log_{10} (x + 5) + 1

, where value of x is:

- 8
3
6
10

Solution: 👈: Video Solution

Concept:

Use the log product rule and the fact that

1=\log_{10}10

.

Explanation:

Given:

\log_{10}5+\log_{10}(5x+1)=\log_{10}(x+5)+1

Replace

1

with

\log_{10}10

.

\log_{10}5+\log_{10}(5x+1)=\log_{10}(x+5)+\log_{10}10

Apply

\log_a m+\log_a n=\log_a(mn)

on both sides.

\log_{10}[5(5x+1)]=\log_{10}[10(x+5)]

Since the logarithms have the same base, equate the arguments.

5(5x+1)=10(x+5)

Divide both sides by

5

.

5x+1=2(x+5)

5x+1=2x+10

5x-2x=10-1

3x=9

x=3

Check domain:

5(3)+1=16>0

and

3+5=8>0

, so

x=3

is valid.

Answer:

x=3

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