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If log5=0.6990 and log3=0.4771, then log45=

Jan 10, 2024

If log5=0.6990 and log3=0.4771, then log45=

Solution by Steps

step 1

Given:

\log(5) = 0.6990

and

\log(3) = 0.4771

. We need to find

\log(45)

step 2

Use the property of logarithms that

\log(ab) = \log(a) + \log(b)

step 3

Since

45 = 5 \times 9

and

9 = 3^2

, we can write

\log(45) = \log(5 \times 9) = \log(5) + \log(9)

step 4

Apply the property

\log(a^b) = b \cdot \log(a)

\log(9)

, where

a = 3

and

b = 2

step 5

\log(9) = \log(3^2) = 2 \cdot \log(3)

step 6

Substitute the given values:

\log(45) = \log(5) + 2 \cdot \log(3) = 0.6990 + 2 \cdot 0.4771

step 7

Calculate the sum:

0.6990 + 2 \cdot 0.4771 = 0.6990 + 0.9542

step 8

Final calculation:

0.6990 + 0.9542 = 1.6532

Answer

\log(45) = 1.6532

Key Concept

Properties of Logarithms

Explanation

The logarithm of a product is equal to the sum of the logarithms of the factors, and the logarithm of a power is equal to the exponent times the logarithm of the base.