Question

What is the solution to the equation 2^ (1 + 2x) = 3 ?


x ≈ –0.292

x ≈ –0.185

x ≈ 0.185

x ≈ 0.292


I got the last one as my answer, am I right? What is the solution to the equation 2^ (1 + 2x) = 3 ?


x ≈ –0.292

x ≈ –0.185

x ≈ 0.185

x ≈ 0.292


I got the last one as my answer, am I right? @Mathematics

Answer 1

All your questions scream "logarithms!" It would be a good idea to review some of their properties. :)

Answer 2

\[\log_2(2^{1+2x})=\log_2(3)\]
\[(1+2x) \log_2(2)=\log_2(3)\]
\[(1+2x)(1)=\log_2(3)\]
\[1+2x=\log_2(3)\]
\[2x=\log_2(3)-1\]
\[x=\frac{\log_2(3)-1}{2}=\frac{\log_2(3)}{2}-\frac{1}{2}=\frac{1}{2} \cdot \frac{\ln(3)}{\ln(2)} -\frac{1}{2}\]

Answer 3

yes last one

Answer 4

Thanks :)