Question

If 3^(x+1)=9^(x+1) find x?

Answer 1

3^ ( x + 1 ) = 3²^(x + 1)

bases are same...

x+1 = 2x + 2

x = -1 Answer

Answer 2

Answer:

$3^{\left(x+1\right)}=9^{\left(x+1\right)}\quad :\quad x=-1$

Step-by-step explanation:

$3^{\left(x+1\right)}=9^{\left(x+1\right)}$

$\mathrm{Convert\:}9^{x+1}\mathrm{\:to\:base\:}3$

$9^{x+1}=\left(3^2\right)^{x+1}$

$3^{x+1}=\left(3^2\right)^{x+1}$

$\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}$

$\left(3^2\right)^{x+1}=3^{2\left(x+1\right)}$

$3^{x+1}=3^{2\left(x+1\right)}$

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

$x+1=2\left(x+1\right)$

$\mathrm{Solve\:}\:x+1=2\left(x+1\right)$

$x+1=2\left(x+1\right)$

$\mathrm{Expand\:}2\left(x+1\right):\quad 2x+2$

$x+1=2x+2$

$\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}$

$x+1-1=2x+2-1$

$\mathrm{Simplify}$

$x=2x+1$

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

$x-2x=2x+1-2x$

$\mathrm{Simplify}$

$-x=1$

$\mathrm{Divide\:both\:sides\:by\:}-1$

$\dfrac{-x}{-1}=\dfrac{1}{-1}$

$\mathrm{Simplify}$

$x=-1$