Question

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

Answer 1

`~~~~~~~4^x = 14 \\\\\implies \ln 4^x = \ln 14\\\\\implies x \ln 4 = \ln 14\\ \\\implies x = (\ln 14)/( \ln 4)\\\\\implies x \approx 1.9037`

Answer 2

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}^{ (3)/(2) } \\ { (√(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`