Question

Shoe that e^3logx is equal to 3x^2

Answer 1

Answer:

Since alogaM=M we have xlog3x+xlog3x=2xlog3x=162=2∗34.

Hence taking logarithms in base 3 we have (log3x)2=4 so (log3x)=2 (for positives) and x=9.

Taking negatives we get x=19

. There are two solutions

Answer 2

Answer:

\frac{dy}{dx}=3x^2

Step-by-step explanation:

Given : y=e^{3\log x}

To find : Show that \frac{dy}{dx}=3x^2 ?

Solution :

We have given,

y=e^{3\log x}

Apply logarithmic property, a\log x=\log x^a

y=e^{\log x^3}

Again applying logarithmic property,e^{\log x}=x

y=x^3

Derivate w.r.t x,

\frac{dy}{dx}=3x^2