Question

1 point

Answer 1

Answer:

$\log_{10}(147) = 2.1673$

Step-by-step explanation:

Given

$\log_{10} 3 = 0.4771$

$\log_{10} 5 = 0.6990$

$\log_{10} 7= 0.8451$

$\log_{10} 11 = 1.0414$

Required

Evaluate $\log_{10}(147)$

Expand

$\log_{10}(147) = \log_{10}(49 * 3)$

Further expand

$\log_{10}(147) = \log_{10}(7 * 7 * 3)$

Apply product rule of logarithm

$\log_{10}(147) = \log_{10}(7) + \log_{10}(7) + \log_{10}(3)$

Substitute values for log(7) and log(3)

$\log_{10}(147) = 0.8451 + 0.8451 + 0.4771$

$\log_{10}(147) = 2.1673$