Rewrite the equation in terms of base e Express the answer i

Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three decimal places.

y = 9(4)^x

Taking natural log of both sides:

ln(y) = ln(9(4)^x)

Log property : ln(A*B) = lnA + lnB

ln(y) = ln9 + ln(4^x)

= ln9 + x*(ln4)

= 2.197 + 1.38x

lny =2.197 + 1.38x

Use the exponent property: lnA = B ----> A = e^B

So, y = e^(2.197 + 1.386x)

= e^(2.197)e^(1.386x)

Exponent Form : y=9e^(1.386x)

ln(y) = ln9 + ln(4^x)

y = e^(ln9 +ln(4^x)

= e^(ln9)e^(xln4)

Natural Logarithm y = 9e^(xln4)

Option B)