Question

what is the approximate value of x in the exponential 4^x=14?

Answer 1

We know 4² = 16 , 4¹= 4

In this case we have :-

${4}^{x} = 14$

and we have to find the value of x

14 is less than 16 so x will be less than 2

14 is greater than 4 so x will be greater than 1

we can find the value of

${4}^{1.5} = {4}^{ \frac{3}{2} } \\ { (\sqrt{4}) }^{3} = {2}^{3} = 8$

so we can say 14 is much larger than 8 which means x will be much larger than 1.5

so according to above ideas we can say our answer is 2nd option which is 1.9037 is our answer

$x \approx1.9037$

Answer 2

$~~~~~~~4^x = 14 \\\\\implies \ln 4^x = \ln 14\\\\\implies x \ln 4 = \ln 14\\ \\\implies x = \dfrac{\ln 14}{ \ln 4}\\\\\implies x \approx 1.9037$