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seropon [69]
3 years ago
10

What is the value of x for log6(5x) + log6(2)=5

Mathematics
1 answer:
Igoryamba3 years ago
8 0

\bf \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_6(5x)+\log_6(2)=5\implies \log_6(5x\cdot 2)=5\implies \log_6(10x)=5 \\\\\\ 6^{ \log_6(10x)}=6^5\implies 10x=6^5\implies x = \cfrac{6^5}{10}\implies x = \cfrac{3888}{5}\implies x = 777.6

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Answer:

The correct answer is the first set {(-1, 8), (0, 5), (2, -1), (3, -4)}

Step-by-step explanation:

In order to determine if the set works, input each ordered pair to see if the statement ends up true. The first two ordered pairs are done below.

(-1, 8)

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8 = 3 + 5

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(0, 5)

f(x) = -3x + 5

5 = -3(0) + 5

5 = 0 + 5

5 = 5 (TRUE)

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