Question

How do you solve `log_3(a+3)+log_3(a-3)=log_3 16`?

Answer 1

`a = +5" " Or" " a=-5`

Explanation:

Solving the given logarithmic equation is determined by applying the multiplication property of logarithm.
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`color(blue)(log(axxb) = loga + logb)`
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`log_3(a + 3) + log_3(a - 3) = log_3 16`
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`rArr color(blue)(log_3 (a + 3)(a - 3) = log_3 16`
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`rArr log_3 (a^2 - 3^2) = log_3 16`
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`rArr log_3 (a^2 - 9) = log_3 16`
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`rArr a^2- 9 = 16`
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`rArr a^2 = 16+9`
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`rArr a^2 = 25`
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`rArr a = +sqrt25" " Or " "a = -sqrt25`
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Hence, `a = +5" " Or" " a=-5`