2^x+2+2^x+1=192

Question

this is solve for x can anyone out there help me please

Answer 1

What if the problem is really 2^(x+2)+2^(x+1)=192 ?

If this is the case we have (2^x)(2^2)+(2^x)(2^1)=192

(2^x)4+(2^x)2=192

6(2^x)=192

2^x=32

x=5(we don't need logs because we know 32 is a power of 2)

check: (2^7)+(2^6)=128+64=192

 

Answer 2

This problem is identical in form to the last one that you asked.

 

you have some:

k^x+k^x+1=c

 

To solve equations of these forms you must recognize that:

k^x+1=k(k^x)

 

this allows you to re-express the original equation as:

k^x+k(k^x)=c

 

factoring you get

k^x(k+1)=c

k^x=c/(k+1)

x=log_k(c/(k+1))

 

Specifically, here you have k=2, and c=192, so:

x=log₂(192/3)

x=log₂(64)

x=6