Solve the equation: 3^x+3 = 2^x (-ln 3)/(ln 6) none (ln...

Transcript

00:01 So we have 3 times the natural log of x plus the natural log of 24 equals the natural log of 3.

00:09 So to solve our variable, we need to have one singular log on our left side and one single log on our right side.

00:15 So basically we need to combine everything.

00:18 So to combine, first we need to look at this first one here.

00:23 We have a coefficient.

00:25 So if you remember, one of the natural log properties is natural log of x to the y power is y times the natural log of x.

00:34 So we're going to undo that.

00:38 So we're going to move our coefficient to our exponent.

00:40 We're just going to do it in reverse.

00:42 So it just becomes the natural log of x cubed.

00:46 And the rest of the problem stays the same.

00:51 So now we want to look at our addition property, the natural log of x.

00:58 What is originally the natural log of x times y becomes the natural log of x plus the natural log of y.

01:06 So because we have addition here, we're just going to have to do that in reverse and turn our addition.

01:10 Into multiplication.

01:13 So this becomes the natural log of x cubed times 24.

01:19 We just do it in reverse equals the natural log of 3.

01:24 So now because we have a singular natural log here and here, we can get rid of those.

01:28 They have just eliminate themselves.

01:30 So we have 24x cubed equals 3...

Solve the equation: \(3^{x+3} = 2^x\) \(\frac{-\ln 3}{\ln 6}\) none \(\frac{\ln 27}{\ln(\frac{3}{2})}\) \(\frac{\ln(\frac{1}{27})}{\ln(\frac{3}{2})}\)