Can someone give 2 examples of a logarithmic equation with infinite solutions?

Mathematics

1 answer:

Vika [28.1K]3 years ago

3 0

Assuming what is meant by "infinite solutions" are infinite number of solutions of a logarithmic equation.

$\frac{1}{2}\log x^2 - \log \sqrt{x} - \log \sqrt{x} = 0$

and

$\frac{1}{2}x-2\ln e^x=-\frac{3}{2}x$

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If (sin(()−1))p =2cos(()−1)q , show that p^2 =4q^2 (1− q^2) ?.

Papessa [141]

Likely the equation is

$\sin^{-1}p=2\cos^{-1}q$

For either side to be defined, we require $|p|\le1$ and $|q|\le1$ . Under these conditions, we can take

$\sin(\sin^{1}p)=\sin(2\cos^{-1}q)$
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$\implies p=2q\sin(\cos^{-1}q)$
$\implies p=2q\sqrt{1-q^2}$
$\implies p^2=4q^2(1-q^2)$

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Given:
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