Question

i need help with this log problem. 2logbase4(5x)=3

Answer 1

Try it first, then I'll help.

Answer 2

What's your 1st step?

Answer 3

well is it log4^3/2=5x?

Answer 4

Almost

Answer 5

But why's the log still there?

Answer 6

see here \[2\log_{4} (5x) \] is equal to 3

Answer 7

oh right. so it would be 4^3/2=5x and then i would have to figure what x is

Answer 8

Yep. So your answer is??

Answer 9

i'm not sure what to do with the fraction

Answer 10

now see according to log law
\[k \log_{a} (n)=\log_{a}(n^k)\]

Answer 11

x^(a/b)=\[(\sqrt[b]{x})^{a}\]

Answer 12

how do i figure x with that?

Answer 13

I gave you a general formula. What is 4^(3/2) using that formula?

Answer 14

yes he is right ANNAZH don't be dependent on any1 fully now try it ur self any problem tell

Answer 15

do i cube or divide 5? im stuck

Answer 16

Leave 5 alone. Forget it for a second.

Answer 17

What is 4^(3/2)? From the formula I gave you above to solve any expression of the form x^(a/b), like this one.

Answer 18

would i changed radical 4 into 2 and then since it has the expo of 2, it is four?

Answer 19

So we have 4^(3/2)...take the square root of 4....and then raise it to the 3rd power. What do you get?

Answer 20

8?

Answer 21

Good. So 5x=8, and thus x=..?

Answer 22

8/5

Answer 23

ahh yes . thanks

Answer 24

\[log_b(a) = k \iff b^k = a\]
Also
\[a\cdot log (b) = log(b^a)\]
Therefore
\[2log_4(5x)=3\]\[\implies log_4([5x]^2) = 3\]\[\implies log_4(25x^2) = 3\]\[\implies 25x^2 = 4^3\]\[\implies x = \sqrt{4^3 \over 25}\]\[\implies x = {2^3 \over 5} = {8 \over 5}\]

Answer 25

Nicely done both of you.