Thread: Exponent rules with logarithms

Hello,

I'm having trouble remembering a basic rule.

The question is:
(e^x)^2 = 3

My next step is:

ln(e^x)^2 = ln(3)

To my understanding, the ln and e knock each other out bringing down the x and 2. My question is, do I add them to make:

x+2 = ln(3) ? I'm not sure about the left side of that equation.

Thanks for any help!

Here's what I got...so unsure about it...

2x = ln(3)
x=1/2 ln (3)
x= 0.549

Originally Posted by shade

Here's what I got...so unsure about it...

2x = ln(3)
x=1/2 ln (3)
x= 0.549

Your calculations are OK. I personally prefer:

Originally Posted by shade

Hello,

I'm having trouble remembering a basic rule.

The question is:
(e^x)^2 = 3

My next step is:

ln((e^x)^2) = ln(3)

To my understanding, the ln and e knock each other out bringing down the x and 2. My question is, do I add them? No

Hello, shade!

Solve for

Take the square root of both sides: .

Take logs: .

Since , we have: .

Originally Posted by shade

Hello,

I'm having trouble remembering a basic rule.

The question is:
(e^x)^2 = 3

My next step is:

ln(e^x)^2 = ln(3)

To my understanding, the ln and e knock each other out bringing down the x and 2. My question is, do I add them to make:

x+2 = ln(3) ? I'm not sure about the left side of that equation.

Thanks for any help!

You are fine until this...



Rules of logs say that the power ("2" in this case) gets brought down as a coefficient...



Now, cancel out the natural log with base e



Solve for x...

Thanks so much for everyone's help!