Question

can someone explain 5^((1-log5(2)) step by step? thanks!

Answer 1

what exactly are you trying to do? are you just simplifying it?

Answer 2

yes please

Answer 3

YEP

Answer 4

5/2

Answer 5

\[5^(1-\log_5(2)) = 5^{(1-(\log(2))/(\log(5))) }\]=5/2

Answer 6

5^((1-log5(2)
5^((1) 5^-log5(2)
5/ 5^(+log5(2))
5/2

Answer 7

Basically, a log function is the inverse of the according exponent function. It took me a fair amount of time after studying log to fully comprehend what this meant. However there are little shortcuts to help until you get to the point that you comprehend what you are doing.

One of the properties of log is if you have:
y=10^(log10)(x))
you can rewrite this as
y=x

In a very oversimplified sense, the 10^ cancels out the log10

This is true in the general case of:
a^loga(b)=b.


Again, when you fully understand log, you will know why this is true but for the meantime it's fine to just memorize the rule.

For this particular problem, you also need to know this exponent rule in it's general form:

x^(a-b)=(x^a)/(x^b)

So know that we know the general forms of the properties, let's apply them to your problem!

5^((1-log5(2))

first, let's use the exponent rule:

5^((1-log5(2))=(5^1)/(5^(log5(2)))

now we we have:

(5^1)/(5^(log5(2)))

next we are going to apply the log rule

(5^1)/(5^(log5(2)))=5/2

Let me know if you have any questions or are confused on any of the steps!