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5.4 Equations Involving Logarithms

Posted on April 21, 2020 by user

METHOD:

For two logarithms of the same base, if $\log_{a} m = \log_{a} n$ , then m = n .
Convert to index form, if $\log_{a} m = n$ , then m = aⁿ.

Example 1
Solve the following equation:
(a)

$\log_{3} 2 + \log_{3} (x + 5) = \log_{3} (3 x - 1)$
(b)

$\log_{2} 8 x - 3 = \log_{2} (2 x - 1)$
(c)

$3 \log_{x} 2 + 2 \log_{x} 4 - \log_{x} 256 = - 1$