For this case we must solve the following equation:
[tex]2 ^ x = 17 ^ x[/tex]
For this, we follow the steps below:
We find the Neperian logarithm on both sides of the equation to remove the variable from the exponent
[tex]ln (2 ^ x) = ln (17 ^ x)[/tex]
We use one of the logarithm properties to extract x from the exponent:
[tex]xln (2) = xln (7)[/tex]
We subtract xln (7) on both sides of the equation:
[tex]xln (2) -xln (7) = 0[/tex]
We take x common factor:
[tex]x (ln (2) -ln (7)) = 0[/tex]
We divide between[tex](ln (2) -ln (7))[/tex]on both sides of the equation, then:
[tex]x = 0[/tex]
Answer:
[tex]x = 0[/tex]
