can u teach me to solve natural log

Question

e^bIna

Answer 1

First look at the exponent “ b ln a “

This is the product of two quantities “b” and “ln a”. 

When can two numbers be multiplied in an exponent? when either is raised to the other power.

 

So this could be expressed as either

 

(e^b)^{ln a}

or

(e^{ln a})^b

 

I’ll choose the second one, because the definition of “ln” is exemplified by 

 

a = e^{ln a}

 

so 

(e^{ln a})^b

is simply 

a^b

 

Does this help?

Answer 2

I can, and would be glad to teach you more. Here recall the property of logarithms that b ln a = ln a^b .

Also recall that  e^{ln x} = x. Thus: e^{b ln a} = e^{ln a^b} = a^b.