contestada

*please help! lots of points and brainiest to right answer!2^x+1 = 5^3x
find the exact solution for x using logarithms and isolating x

Respuesta :

[tex]\\ \rm\Rrightarrow 2^{x+1}=5^{3x}[/tex]

[tex]\\ \rm\Rrightarrow ln2^{x+1}=ln5^{3x}[/tex]

[tex]\\ \rm\Rrightarrow (x+1)ln2=3xln5[/tex]

[tex]\\ \rm\Rrightarrow xln2+ln2=3xln5[/tex]

[tex]\\ \rm\Rrightarrow ln2=3xln5-xln2[/tex]

[tex]\\ \rm\Rrightarrow ln2=x(3ln5-ln2)[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{ln2}{3ln5-ln2}[/tex]