Help with Indices: how to solve 4^(x-1) = 5^x

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shaoen01

New member
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Aug 22, 2006
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25
How do i solve the equation below?

Qns:
\(\displaystyle 4^{(x-1)} = 5^x\)

My Working:
\(\displaystyle 4^{(x-1)} = 5^x\)
\(\displaystyle 2^{2(x-1)} = 5^{x}\)

And basically i am stuck here. How do i solve the equation above if i am unable to get a similar base? What should i do?
 
Use properties of logs.

\(\displaystyle \L\\ln(4^{x-1})=ln(5^{x})\)

\(\displaystyle \L\\(x-1)ln(4)=xln(5)\)

Can you finish up now?.
 
shaoen01 said:
\(\displaystyle 4^{(x-1)} = 5^x\)
Click to expand...

Just another contortion:

4^x 4^(-1) = 5^x
5^x / 4^x = 1 / 4
(5/4)^x = 1/4
x = log(1/4) / log(5/4)
 
shaoen01 said:
Yup, i got the answer from sosmaths too. Thanks
Click to expand...
Just for the record, this behavior (posting the same question in multiple locations) normally is considered bad form. It wastes the time of volunteers. I realize it may save a few moments of your time, but let's think about that choice just a bit more.

Thanks
 
Hi,

Sometimes both sides give me different types of working and it helps me to understand better. That's why i post in 2 forums to compare the workings and see which is easier for me to understand.

I didn't mean to waste volunteers' time and effort. I just wanted to find out if there is another way of doing an equation.
 
Just ask, but not in multiple locations. You are considering your time of more value than the time of the volunteers. If you need clarification or expansion, simply ask. "Is there another way to approach this?" "My teacher did some werd thing with an exponent of 2." "Why did you select that methodology?" They are called questions. Feel free to use them.

It's like this:

If two volunteers are writing an answer at the same time, it is very likely one of them is wasting his/her time. You might get slightly different answers, but that is not very likely at all. It is very frustrating to spend time on an answer, only to discover that someone else already supplied an appropriate response. Multiple posts make this problem much more likely. It is bad enough with a single post! Making it worse is not a good idea. The tiny hope of additional personal benefit is far outweighed by the potential frustration of the volunteers. It's not even a close contest.
 
Hi,

I apologize if i have wasted any volunteers' time, I did not have ill intentions but my way of execution is wrong. I'll make sure there won't be a next time.
 
Learning is what we do here. Getting along is an important part of that.
 
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