The question is in the picture. please help

Mathematics

2 answers:

tresset_1 [31]3 years ago

8 0

The 50th term would be 317

maks197457 [2]3 years ago

3 0

Answer:

50th term would be 317

Step-by-step explanation:

The "shortcut" would be 17+6x since you have a starting value of 17 and you add 6 to each term.

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

Ray Of Light [21]

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.