Logarithm exam questions

[Barbie]

Hello everyone.Help with these please.Solve and show me explanation for all thanks.

1. In(1+x^2) = 1+2Inx

2. e^x = 3^(x-2)

3. 4^(3x-1) = 3(5^x)

4. e^x + e^(2x) = e^(3x)

5. In(2 + e^-x ) = 2

6. 2 log2 x = 3 + log2 (x+1)

 

[topsquark]

We aren't here to do your homework. What have you been able to do with these? We'll be able to help you better if we know where you are getting stuck.

-Dan

 

[Deleted member 4993]

Hello everyone.Help with these please.Solve and show me explanation for all thanks.

1. In(1+x^2) = 1+2Inx

2. e^x = 3^(x-2)

3. 4^(3x-1) = 3(5^x)

4. e^x + e^(2x) = e^(3x)

5. In(2 + e^-x ) = 2

6. 2 log2 x = 3 + log2 (x+1)

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

Please post one problem/post - including your thoughts/work. Tell us exactly where you are stuck!

 

[HallsofIvy]

I will give you a couple of hints.

[math]e^{3x}= (e^x)^3[/math]. and

\(\displaystyle 2ln(x)= ln(x^2)\).

 

[Steven G]

Hello everyone.Help with these please.Solve and show me explanation for all thanks.

1. In(1+x^2) = 1+2Inx

2. e^x = 3^(x-2)

3. 4^(3x-1) = 3(5^x)

4. e^x + e^(2x) = e^(3x)

5. In(2 + e^-x ) = 2

6. 2 log2 x = 3 + log2 (x+1)

I'll get you started.
1 =lne
In(1+x^2) = 1+2Inx
In(1+x^2) = lne+2Inx
In(1+x^2) = lne+Inx²
In(1+x^2) = In(ex²)
(1+x^2) = (ex²)
Now solve this equation


Alternate method.
In(1+x^2) = 1+2Inx
In(1+x^2) -2Inx=1
In(1+x^2) -Inx²=1
In[(1+x^2)/x²]=1
Write in exponential form and solve for x.

Now do the others and show your work.

 

[Dr.Peterson]

1. In(1+x^2) = 1+2Inx

I'll get you started.
1 =lne
In(1+x^2) = 1+2Inx
In(1+x^2) = lne+2Inx

No!

\(\displaystyle ln(1 + x^2) \ne 1 + 2ln(x)\)

I had the same wrong impression of Jomo's work when I first looked at it; then I realized that the second line is simply the equation being solved, not an implication from the first. The work is fine.

 

[lookagain]

I had the same wrong impression of Jomo's work when I first looked at it; then I realized that the second line is simply the equation being solved,
not an implication from the first. The work is fine.

I deleted my wrong post.