How do you evaluate $\log _ { 3} 2+ 3\log _ { 3} 4$ ?

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Answer 1 · 2017-08-06T09:58:11

$4.4165$

If you are adding logs with the same base, it it the same as multiplying the numbers.

$log_3 2 + 3log_3 4" "larr$ apply the power law.

$=log_3 2 + log_3 4^3$

$=log_3 (2 xx 64)$

$log_3 128$

$128$ is not a power of $3$ , so to continue requires a calculator.
We can estimate the answer:

$3^4 = 81 and 3^5 = 243$ , so the value has to be between $4 and 5$

Using the change of base law:

$(log_10 128)/(log_10 3)$

$=4.4165$

How do you evaluate \log _ { 3} 2+ 3\log _ { 3} 4\log _ { 3} 2+ 3\log _ { 3} 4?