exponential equation: 5^x=3^x+1

[jshaziza]

5^x=3^x+1
So far what I was able to figure out was this:
log 5^x=log 3^x+1
x log 5=x+1 log 3
If someone could show me the next step after this that should be enoug. thx.

 

[Deleted member 4993]

Re: exponential equation

5^x=3^x+1
So far what I was able to figure out was this:
log 5^x=log 3^x+1
x log 5=x+1 log 3
If someone could show me the next step after this that should be enoug. thx.

What is the problem asking you to do?

You have not stated that.

 

[stapel]

5^x=3^x+1

As posted, the above means the following:

. . . . .5^x = 3^x + 1

Is this what you meant?

Also, what were the instructions? What are you trying to accomplish?

Please be specific. Thank you!

Eliz.

 

[soroban]

Re: exponential equation

Hello, jshaziza!

5^x .= .3^x+1

So far what I was able to figure out was this:

. . log (5^x) .= .log(3^x+1)

. . x·log(5) .= .(x+1)·log(3) . . . . Good!

Mutliply out the right side: .x·log(5) .= .x·log(3) + log(3)

Then: .x·log(5) - x·log(3) .= .log(3)

Factor: .x·[log(5) - log(3)] .= .log(3)

. . . . . . . . . . . . . . . . log(3)
Therefore: .x .= .--------------- .= .2.150660103
. . . . . . . . . . . . .log(5) - log(3)

 

[jshaziza]

Sorry about that, it tells me to solve the equation.