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Vadim26 [7]
2 years ago
5

Solve log base 6 (x-6) - log base 6 (x + 4) = 2

Mathematics
1 answer:
Ray Of Light [21]2 years ago
4 0

Answer:

no solutions

Step-by-step explanation:

Since the two terms have the same base, we are able to use the rule for subtracting logarithms:

log_{b}(x) - log_{b}(y) = log_{b}(\frac{x}{y} )

Therefore, the equation can be written as:

log_{6}(\frac{x-6}{x+4} )=2

By using the definition of a logarithm we can say that:

\frac{x-6}{x+4} = 6^{2}\\\frac{x-6}{x+4} = 36\\x -6 = 36x+144\\35x = -150\\x =-\frac{30}{7}

When plugging this solution in, you find that the term log_{6}(x-6) has x-6 evaluate to a number less than 0. This is not included in the domain of log functions, so -\frac{30}{7} is not a valid solution. This means that there are no solutions.

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