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

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2 Answers

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
 
This problem is identical in form to the last one that you asked.
 
you have some:
kx+kx+1=c
 
To solve equations of these forms you must recognize that:
kx+1=k(kx)
 
this allows you to re-express the original equation as:
kx+k(kx)=c
 
factoring you get
kx(k+1)=c
kx=c/(k+1)
x=logk(c/(k+1))
 
Specifically, here you have k=2, and c=192, so:
x=log2(192/3)
x=log2(64)
x=6