how can I solve log (3x) = log 2 + ( x-1)

Question

LOGARITHMIC EQUATIONS

Answer 1

If the word log was left out, then the equation should be log(3x)=log2+log(x-1)

log(3x)=log3+log(x)

log3+log(x)=log2+log(x-1)

log3=0.47712 and log2=0.30103

0.47712+log(x)=0.30103+log(x-1)

0.47712-0.30103=log(x-1)-log(x)

0.17609=log[(x-1)/(x)]

log1.5=0.17609

therefore log(1.5)=log[(x-1)/(x)]

                      1.5=(x-1)/(x)

                      1.5x = x-1

                      1.5x - x = -1

                                0.5x = -1

                                     x = -1/(0.5)

                                     x = -2

Answer 2

Did you leave out part of the problem?  

 

Was the problem really this?

log (3x) = log 2 + log( x-1)

 

log (3x) = log (2*(x-1))

 

3x = 2x -2 

 

Subtract 2x from each side.

x = -2

 

 

It's a very strange problem if you didn't leave off the "log" from the (x-1).

Answer 3

I don't see a way to solve this question directly and exactly. 

 

There are still several ways to find a solution, though.

 

Some of the ways are:

 

a) Graphing two expressions to see where they intersect

 

b) using Taylor series to expand the new expression in terms of a power series, neglecting the higher order terms

 

c) use Newton's method to find solution

 

d) use one of several other iterative techniques

 

The one you should use depends on the context, where is this question coming from? what methods are being discussed or demonstrated in the text or lessons preceding it?