Question

3^2 x 3^x =3^7 find the value of x

Answer 1

Answer:

x = 5

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Step-by-step explanation:

$\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}$

$3^x\cdot \:3^2=3^{x+2}$

$3^{x+2}=3^7$

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

$x+2=7$

$\mathrm{Solve\:}\:x+2=7:\quad x=5$

$\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}$

$x+2-2=7-2$

$Simplify$

$x=5$

So, x = 5

Answer 2

3^2 • 3^x=3^(2+x)

3^(2+x)=3^7

=> 2+x=7

x=5