SOLUTION: Solve the following exponential equations using logarithms: 2^(x) = 3^(x+1) Feeling pretty lost on this one... I've tried to google for similar examples, but when I do find

Question 408682: Solve the following exponential equations using logarithms:
2^(x) = 3^(x+1)
Feeling pretty lost on this one...
I've tried to google for similar examples, but when I do find a similar problem it's solves using a form like this: "xln(2)=(xln(3)+ln(3))" I think this is a little beyond where I am now :( Looking for a more basic algebra solution!
Appreciate any help!!
Thanks :)
Found 2 solutions by richard1234, jim_thompson5910:
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
The ln function shouldn't be too far beyond your reach, since ln is a logarithm function (except it uses the base , where e = 2.71828.... e is a very important number in calculus).

The easiest way to solve this is to isolate the 1 on the exponent x+1 to obtain

Divide both sides by

Take the log base 2/3 of both sides to obtain

= -2.709511...
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If something like "xln(2)=(xln(3)+ln(3))" scares you, then just replace each "ln" with "log" and you'll get

xlog(2)=xlog(3)+log(3)

Why can I replace "ln" with "log"? Because "ln" is actually a log that has base 'e' (2.718...). However you can use any log of any base. So you can use the default log of base 10 if you want.

If you need more help, email me at jim_thompson5910@hotmail.com

RELATED QUESTIONS
Solve the following exponential equations using Logarithms. Round to 3 decimal places.... (answered by stanbon,Theo)
im so lost with this one... Solve the exponential equation. express the solution set... (answered by Alan3354,jsmallt9)
Hi! Given that x^2-14x+a=(x+b)^2 for all values of x, find the value of a and the... (answered by reviewermath,Okeke_Christian)
Solving Exponential Equations Using Logarithms? 2^x = 30 5^x - 1 = 3^x 3.53^(x+1)... (answered by edjones)
Solve the following system of equations {x+5/4y-5/2=0 {x+1/5=-y This is a question on... (answered by josgarithmetic)
This one is really stumping me... Havent got into the ln function yet, only using log... (answered by Alan3354)
Solve the inequality (x-2)^2(x+1)^3(x-5) <_0 if you could please thoroughly explain it (answered by Fombitz)
Please help me solve this problem: There are two hoses filling up a pool. The two hoses... (answered by ikleyn)
Solve the following quadratic equations. 4x^2=13x+12... (answered by HyperBrain,stormy)