A Complicated Logarithm Problem

Algebra 2 Tutorial

A Complicated Logarithm Problem


I hope you know that the following theorems are true


log_ax + log_ay = log_a(x*y)

log_ax - log_ay = log_a(x/y)

We are going to use all of these theorems to simplify a complicated logarithm expression

Sample Problem

simplify the following expression




log_2(16x^5) - log_2\sqrt[3]{y} ….. because log_a(b/c)} = log_ab - log_ac

log_216 + log_2x^5 - log_2\sqrt[3]{y} …… because log_2(16x^5) = log_216 + log_2x^5

4 + 5log_2x - log_2\sqrt[3]{y} ….. because log_216 = 4 and ……………………………………………….log_2(16x^5) = 5log_2(x)

4 + 5log_2x - log_2y^{(1/3)} … because log_2\sqrt[3]{y} = log_2y^{(1/3)}

4 + 5log_2x - (1/3)log_2y …. because log_2y^{(1/3)} = (1/3)log_2y

The expression log_2\frac{16x^5}{\sqrt[3]{y}} looks very different than the expression 4 + 5log_2x - (1/3)log_2y , but in fact the algebra above shows them to be completely equivalent

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