Solve the equation: ${ 2 }^{ x }+{ 2 }^{ x+1 }+{ 2 }^{ x+2 }+{ 2 }^{ x+3 }=\frac { 15 }{ 2 }$.
+539 15/2 = 7.5
Adding multiples of 2 we can never get 1/2 unless we use an exponent of -1 at one point.
Having exponents smaller would result in longer decimals(.25,.125) So x has to be -1
Checking we get
2^-1+2^0+2^1+2^2
1/2+1+2+4
1/2+7
7.5
+267 just ignore the base and just look at the exponent
so the equation becomes (x)+(x+1)+(x+2)+(x+3)=15/2.
combine like terms -> 4x+6=15/2
subtract 6 from both sides and divide both sides by 4 to get x=3/8
+240 \(2^x+2^{x+1}+2^{x+2}+2^{x+3}=\frac{15}{2}\)
\(15\cdot \:2^x=\frac{15}{2} \)
\(\frac{15\cdot \:2^x}{15}=\frac{\frac{15}{2}}{15}\)
\(2^x=\frac{1}{2}\)
\(x=-1\)
