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Artist 52 [7]
2 years ago
5

(4Q) If c < d and x > 1, which of the following must be true?

Mathematics
1 answer:
scoray [572]2 years ago
3 0

Use the rule to change the base

\log_a(b) = \dfrac{\log_c(b)}{\log_c(a)}

To express both logarithms in terms of the natural logarithm (for example, any common base would be fine:

\log_c(x) = \dfrac{\ln(x)}{\ln(c)},\quad \log_d(x) = \dfrac{\ln(x)}{\ln(d)}

Since the natural logarithm is an increasing function, we have

c\ln(d)

which implies

\dfrac{\ln(x)}{\ln(c)}=\log_c(x)

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