Test Index

Logarithms Practice Test 1

© examsnet.com

Question : 12 of 40

Marks: +1, -0

If

\log_{10} 3 = 0.477

, the number of digits in

3^{50}

is:

23
24
50
150

Solution: 👈: Video Solution

Concept:

For a positive number

N

, if

\log_{10} N = m

, then the number of digits is

\lfloor m \rfloor + 1

.

Explanation:

Let

N = 3^{50}

.

Taking log base

10

:

\log_{10} N = 50 \log_{10} 3

.

Substitute

\log_{10} 3 = 0.477

:

\log_{10} N = 50 \times 0.477 = 23.85

.

So

\lfloor 23.85 \rfloor = 23

.

Number of digits

= 23 + 1 = 24

.

Answer:

The number of digits in

3^{50}

is

24

.

© examsnet.com

Go to Question:

Prev Question

Next Question