Question

Find the value of x, 3^{2x}=3^{x+5}

Answer 1

Answer:

$3^{2x}=3^{x+5}\quad :\quad x=5$

Step-by-step explanation:

$3^{2x}=3^{x+5}$

$\mathrm{If\:}a^{f\left(x\right)}=a^{g\left(x\right)}\mathrm{,\:then\:}f\left(x\right)=g\left(x\right)$

$2x=x+5$

$\mathrm{Solve\:}\:2x=x+5$

$2x=x+5$

$\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}$

$2x-x=x+5-x$

$\mathrm{Simplify}$

$x=5$

Answer 2

Answer:

5

Step-by-step explanation:

According to the given question,

• 3^(2x) = 3^(x+5)

Taking log both sides, we get

• log 3^(2x) = log 3^(x+5)

• 2x × log 3 = (x+5) × log 3

log 3 both sides get cancelled out,

• 2x = x+5

• x = 5 ans.

Thus value of x = 5