color(blue)("Introduction of concepts"
Example of principle: Try this on your calculator
Using log to base 10 enter log(10) and you get the answer of 1.
Log to base e is called 'natural' logs and is written as ln(x) for any value x
color(brown)("Consequently "ln(e)=1) Try that on your calculator
[ you may have to enter ln(e^1) ]
Another trick is that log(x^2) -> 2log(x) => ln(x^2)=2ln(x)
Combining these two ideas:
ln(e^2)" "=" "2ln(e)" "=" "2xx1=2
color(brown)("So "ln(e^x)" "=" "xln(e)" "=" "x xx1" " =" " x)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Solving the question")
Given:" "e^x+3=6
Subtract 3 from both sides
" "e^x=6-3
" "e^x=3
Take logs of both sides
" "ln(e^x)=ln(3)
" "xln(e)=ln(3)
But ln(e)=1 giving
color(green)(x=ln(3) ~~1.099" to 3 decimal places")
