Question

The number of real solutions of the equation ${\left(\frac{3}{5}\right)}^x+\frac{7}{5}=2^x$ is

• A. 2
• B. 1
• C. 0
• D. infinite

Answer 1

Answer: (B)

1

Let take $f\left(x\right)={\left(\frac{3}{5}\right)}^x+\frac{7}{5}-2^x$
$f^{\prime }\left(x\right)$ will always negative so this function is continuously decreasing, thus it will intersect at once to $x-axis$.
Hence only one root exists.