Properties of logarithms Calculator

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Example

Created on 2024-06-20Asked by Scarlett Ramirez (Solvelet student)

Simplify the expression:

\log_a(xy)

Solution

To simplify the expression

\log_a(xy)

: 1. Use the property of logarithms:

\log_a(xy) = \log_a(x) + \log_a(y).

Therefore,

\log_a(xy) = \log_a(x) + \log_a(y)

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Some of the related questions asked by Luna Jackson on Solvelet

1. Simplify the expression

\log_2(8) - \log_2(2)

.2. Solve the equation

\log_3(x) = 2

for

x

DefinitionLogarithms have important properties such as the product rule logb(xy)=logb(x)+logb(y), the quotient rule logb(yx)=logb(x)−logb(y), and the power rule logb(xy)=ylogb(x) that provide us with tools for simplifying and manipulating complex logarithmic expressions. Examples: Employ the product rule, log(2⋅5)=log(2)+log(5)

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