Question

Which of the following is the greatest?
a.2^150
b.3^125
c.4^100
d.9^75

Answer 1

Hey Graxia! Welcome to OpenStudy! You question, quick question about it, is this what it's supposed to look like? \[2^{150}\] \[3^{125}\] \[4^{100}\] \[9^{75}\] That's what you mean, right? From A-D

Answer 2

Use calculator.

Answer 3

So it's easiest to put them in ur calculator and compare which number is the largest! :)

Answer 4

Look: \(2^3 < 3^2\). For example we can then say that \((2^3)^{10} < (3^2)^{10}\). etc.
This kind if inequality might the trick to solve this question.

Answer 5

might be*

Answer 6

we look at 150 and 125. they are multiples of 25.
then, thinking of the same trick, we look for \(m\) and \(n\) such that
\(125=n\times 25\), \(150=m\times 25\).
we have \(n=5,m=6\).
therefore, if \(2^{6}<3^5\) is true, then we have shown that \((2^{150}<3^{125}\)).

Answer 7

@Graxia and this seems to be the method for finding easily the biggest of them.

Answer 8

test \(3^5\) vs \(4^4\) vs \(9^3\).

Answer 9

@andriod09 yes that's what I mean

Answer 10

Complex equations, not very good right? Do you have a graphing calculator on hand, by any chance?

Answer 11

Express each in an exponential form with the same exponents and compare the resulting bases , which one is the largest base?

Answer 12

yes, you could call it like that.
Since \(2^{6}<3^5<4^4<9^3\), the answer is …

Answer 13

it's like that*

Answer 14

Oh so ur trying to solve it by hand?

Answer 15

Graxia, if you're trying to solve it by hand, then just look, which one do you think is bigger? All you have to really do is look at the base number, not the exponent, right @reemii?

Answer 16

@reemii yes like that , so which one of that is the largest base ?

Answer 17

by hand you can see that \(9^3\) is the largest.

Answer 18

(D) is the answer.i
I it completely clear? @Graxia

Answer 19

Yes you are:)

Answer 20

Is*
lol ok