Question

guys answer this.. Check the pic above.
Find the 'x' in that... With steps!! ​

Answer 1

Answer:

$\blue{3^x+3^{x+1}=36\quad :\quad x=2}$

Step-by-step explanation:

$3^x+3^{x+1}=36$

$\black{\mathrm{Factor\:}3^x+3^{x+1}:}$

$3^x+3^{x+1}$

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

$\gray{3^{x+1}=3^1\cdot \:3^x}$

$=3^x+3^1\cdot \:3^x$

$\gray{\mathrm{Factor\:out\:common\:term\:}3^x}$

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

$\gray{\mathrm{Refine}}$

$=4\cdot \:3^x$

$4\cdot \:3^x=36$

$\gray{\mathrm{Divide\:both\:sides\:by\:}4}$

$\frac{4\cdot \:3^x}{4}=\frac{36}{4}$

$\gray{\mathrm{Simplify}}$

$3^x=9$

$\gray{\mathrm{Convert\:}9\mathrm{\:to\:base\:}3}$

$\gray{9=3^2}$

$3^x=3^2$

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

$x=2$