Question

HELP ASAP! Find solutions (MULTIPLE) for the equation:
6^x+2=8
E is a correct answer, I need help finding the others
(100 points!!)

Answer 1

Answer:

$x = \frac{3in(2)}{in(6)} - 2$

Solving steps:

$-›6 {}^{x + 2} = 8$

Apply exponents rule

$-›(x +2)in(6) = in(8)$

Solve for (x + 2) in(6) = in(8)

$-›x = \frac{3in(2)}{in(6)} - 2$

Answer 2

$\\ \rm\rightarrowtail 6^{x+2}=8$

$\\ \rm\rightarrowtail (6)^{x+2}=2^3$

$\\ \rm\rightarrowtail ln6^{x+2}=ln2^3$

$\\ \rm\rightarrowtail (x+2)ln6=3ln2$

$\\ \rm\rightarrowtail xln6+2ln6=3ln2$

$\\ \rm\rightarrowtail xln6+2ln2+2ln3=3ln2$

$\\ \rm\rightarrowtail xln6+2ln3=3ln2-2ln2$

$\\ \rm\rightarrowtail xln6+2ln3=ln2$

$\\ \rm\rightarrowtail xln3+xln2+2ln3=ln2$

$\\ \rm\rightarrowtail (x+2)=\dfrac{ln8}{ln6}$

$\\ \rm\rightarrowtail x=\dfrac{ln8}{ln6}-2$

Another

$\\ \rm\rightarrowtail (x+2)ln6=ln8$

$\\ \rm\rightarrowtail (x+2)ln6=ln2^3$

$\\ \rm\rightarrowtail (x+2)ln6=3ln2$

$\\ \rm\rightarrowtail x+2=\dfrac{3ln2}{ln6}$

$\\ \rm\rightarrowtail x=\dfrac{3ln2}{ln6}-2$