Question

x is a real number and 16^(x) =4^(3) ; what is the value of x? a) 1/ 2 b) 3/2 c) 3 d) 4 e) 9 Can you deeply explain to me, please? Thanks

Answer 1

do you mean \[\frac{x}{16} = \frac{3}{4}\]

Answer 2

Get the base same.

\(\Large \color{Black}{\Rightarrow (4^2)^x = 4^3 }\)

\(\Large \color{Black}{\Rightarrow 4^{2x} = 4^{3} }\)

Equate the exponents.

\(\Large \color{Black}{\Rightarrow 2x = 3 }\)
\(\Large \color{Black}{\Rightarrow x = 1.5 = {3 \over 2} }\)