Natural Logarithms

[Angela123]

11(8^x)=1.5e^3x

I tried dividing both sides by 1.5 then I was left with:
(11/1.5)(8^x/1.5)=e^3x

I then took the ln of everything and I was left with:
ln(11/1.5)+ln(8^x/1.5)=3x

Now I am stuck and need help.

 

[wjm11]

11(8^x)=1.5e^3x

I tried dividing both sides by 1.5 then I was left with:
(11/1.5)(8^x/1.5)=e^3x

I then took the ln of everything and I was left with:
ln(11/1.5)+ln(8^x/1.5)=3x

Hello, Angela,

Your approach is correct, though you have an error. Only divide 11(8^x) by 1.5 once. Do not divide both the 11 and the 8^x by 1.5:

(11/1.5)(8^x) = e^3x
ln(11/1.5)+ln(8^x) = 3x

Since x is an exponent in ln(8^x), it can be moved to the coefficient position:

ln(11/1.5) + x*ln(8) = 3x

Now move all your x terms to one side of the equation and factor:

ln(11/1.5) = 3x – xln(8) = x(3 – ln8)

Can you take it from here?