1. ## Logarithm equations

I have encountered an equation for logarithms and the guide in the book didn't make sense to me.
Here's the equation: 3^(x+2)=4^(x-1)

And here's how the book explained it:
1) Take log of each side: log3^(x+2)=log4^(x-1)
2)Take exponents to the front: x+2log3=x-1log4
and here's where it starts not making sense to me,
3)divide each side by 2log3: 2x=(-1log4)/(2log3)

How did the equation suddenly become 2x and why wouldn't it become (x+2)log3=(x-1)log4?

2. Originally Posted by windia
I have encountered an equation for logarithms and the guide in the book didn't make sense to me.
Here's the equation: 3^(x+2)=4^(x-1)
How did the equation suddenly become 2x and why wouldn't it become (x+2)log3=(x-1)log4?
The part in blue is correct.
So use it to finish.

3. 3^(x+2)=4^(x-1)

we take log from both sides:

log3^(x+2)=log4^(x-1)

(x+2)log3=(x-1)log4

xlog3+2log3=xlog4-log4

x(log3-log4)=-log4-2log3

.
.
.

4. Wow good thing I trusted my instincts. I'm through with this book haha. Thanks you guys