Math Help - Exponential and Logarithmic Equations

1. Exponential and Logarithmic Equations

Hey guys,

Solve the equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.
You don't have to do the decimal part.

the answer is log (0.2) / (log3 - log0.2)

0.2^X+1 = 3^X

what I did is

x+1Log 0.2 = xLog3

and then i divided Log 0.2 from both sides but that doesn't work.

2. Re: Exponential and Logarithmic Equations

Use brackets when your indexes are more than 1 letter.
You correctly took logs of both sides. Your equation (x+1)Log 0.2 = xLog3 is just like (x+1)A = xB, find x from that like you normally would.

3. Re: Exponential and Logarithmic Equations

Originally Posted by Shakarri
Use brackets when your indexes are more than 1 letter.
You correctly took logs of both sides. Your equation (x+1)Log 0.2 = xLog3 is just like (x+1)A = xB, find x from that like you normally would.

okay, so I divide log 3 on both sides which gets me x+1Log0.2 / Log3

but the answer is (0.2) / (log3 - log0.2)

what do I do with the x + 1 ?

4. Re: Exponential and Logarithmic Equations

$\frac{(x+1)Log0.2}{Log3}=x$

$x\frac{Log0.2}{Log3}+\frac{Log0.2}{Log3}=x$

Solve for x

5. Re: Exponential and Logarithmic Equations

Oh man, sorry, but I'm completely lost. I don't know how you got two terms. Also, I have no idea how to solve for x right there.

6. Re: Exponential and Logarithmic Equations

Log of a number is a constant, its just like any other number you'd get in an equation.

7. Re: Exponential and Logarithmic Equations

Ohhhhhh so you just distributed the (x+1) with Log0.2 I see.
ahh, I see. So, now I move Log0.2 / Log3 to the right of the equation? Now, I have xlog0.2/log3 = - log0.2/log3

I don't think that's correct :\

8. Re: Exponential and Logarithmic Equations

You were told in Shakarri's first response that this is the same as A(x+ 1)= Bx (with A= log(0.2) and B= log(3)). That is the same as Ax+ A= Bx so, subtracting Ax from both sides A= (B- A)x. Can you solve that?

9. Re: Exponential and Logarithmic Equations

Yes, I got log0.2 = (log3 - log0.2)x / log0.2

it's just reversed. log0.2 has to be on top.