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elixir [45]
3 years ago
12

How to do this?

Mathematics
1 answer:
Mandarinka [93]3 years ago
7 0
This equation uses two properties of logarithms:

\ln(g^x) = x \ln(g)

\ln(a) + \ln(b) = \ln(ab)

So you could take the ln from left and right hand side in the equation, and get:

(2-x)ln 3 = x ln 5

then

2 ln 3 - x ln 3 - x ln 5 = 0 =>

x(ln 3 + ln 5) = 2 ln 3

so x = 2 ln 3 / (ln3 + ln5)

Now using the 1st property you can say 2 ln 3 is ln 3² = ln9
and using the 2nd property you can say ln3 + ln5 = ln15

so x= ln9 / ln15


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