Question

How can I prove `b^(x+y)=b^xb^y` by using `b^x=e^(xln(b))` ?

Answer 1

`\`

`"Please see proof below."`

Explanation:

`\`

`"We compute as follows, using the rule you provided,"`
`"to be taken as a given:"`

`b^{x+y} \ = \ e^{ (x+y) ln(b) } \ = \ e^{ [ x ln(b)+ y ln(b)] } \ = \ e^{ x ln(b) } \cdot e^{ y ln(b) }`

`\qquad \qquad \ = \ b^{x} \cdot b^{y}. \qquad \qquad \qquad square`