Finding x in a sum of exponents of the same base

Question

This one has me stumped. I know that there is no law of exponents explaining what happens for a sum of exponents with the same base, so I tried taking the natural log on both sides and adding the exponents that way as they multiply the same base, but it doesn't seem to be correct and I haven't been able to find a good explanation for how to proceed.

The problem is: 2^(x+2) + 2^(x+1) + 2^(x) = 3/4

If this question is against any of SE's rules I would be more than pleased to know of a good source to learn how to solve these types of problems, or even simply a nudge in the right direction! Thanks.

Answer 1

write $$2^x\cdot 2^2+2^x\cdot 2+2^x=\frac{3}{4}$$ can you finish?

Answer 2

$$ 2^{x+2} + 2^{x+1} + 2^x = 3/4 $$

$$ 4 (2^x) +2(2^x) + 2^x = 3/4 $$

Let $y=2^x$ and substitute to get $$ 7y=3/4 $$

$$ y= \frac{3}{28}$$

$$2^x= \frac{3}{28}$$

$$ x \ln(2) = \ln(\frac{3}{28})$$

Solve for $x$.