Question

Solve 4^x- 3 = 18. Round to the nearest thousandth.

Answer 1

4^(x- 3) = 18

ln[4^(x- 3)] = ln(18)

ln4(x - 3) = ln(18)

ln4x - ln4(3) = ln18

ln4x = ln18 + 3ln4

x = [ln18 + 3ln4]/ln4

x = 5.0849625007

x is approximately 5.085.

Answer 2

Logarithm functions are the inverse of the exponential functions. Using the logarithm functions property we get the value of the x for the given function is 5.079(approx.).

Given-

The function given in the problem is,

$4^{(x-3)}=18$

What is the logarithm function?

Logarithm functions are the inverse of the exponential functions. Solve the given problem using the properties of the logarithm functions,

$4^{(x-3)}=18$

Taking log both side,

$ln [4^{(x-3)}]=ln (18)$

$(x-3)ln(4)=ln(18)$

$(x-3)=\dfrac{ln(18)}{ln(4)}$

$(x-3)=\dfrac{2.8903}{1.3862}$

$(x-3)=2.079$

$x=2.079+3$

$x=5.079$

The value of the x for the given function is 5.079(approx.).

Learn more about the logarithm function here:

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