Question

Determine o conjunto verdade:

a) (2/3)^x = (8/7)

b) (9/25)^2x = (3/5)

c) 5^x = $\sqrt{5}$

Answer 1

Olá, Nathalia.

$a)~(\frac23)^x=\frac87\Rightarrow x=\log_{\frac23}\frac87=\frac{\log\frac87}{\log\frac23}=\boxed{\frac{\log8-\log7}{\log2-\log3}}$

$b)~(\frac9{25})^{2x}=\frac35\Rightarrow [(\frac35)^2]^{2x}=\frac35\Rightarrow(\frac35)^{4x}=(\frac35)^1\Rightarrow4x=1\Rightarrow\boxed{x=\frac14}$

$c)~5^x=\sqrt5\Rightarrow5^x=5^{\frac12}\Rightarrow\boxed{x=\frac12}$