Question

if log(subscript:b)x = 0.34 and log(subscript:b)z = 0.85, evaluate the following expression: log(subscript:b)((sqrt(x)/(cubedsqrt(z))

Answer 1

really need the answer please !

Answer 2

You have:\[\log_{b}(x)=0.34,\]\[\log_{b}(z)=0.85,\]\[\log_{b}(\frac{\sqrt{x}}{\sqrt[3]{z}}).\]

Answer 3

\[log_{b}\frac{\sqrt{x}}{\sqrt[3]{Z}}\]
use the logarithm rules to break them up into log x and log z, which you know the values of.

\[log_{b}\frac{x}{y}=log_{b}x-log_{b}y\]
\[log_{b}x^{a}=alog_{b}x\]

Answer 4

log identities:\[\log a + \log b = \log (ab)\]\[\log a - \log b = \log (a/b)\]\[a \log b = \log b^{a}\]

Answer 5

also useful:
\[\sqrt[a]{x}=x^{\frac{1}{a}}\]

Answer 6

is the answer -0.3642??

Answer 7

That's not what I got. What expression did you eventually simplify it to?

Answer 8

yeah i don't think that's write which is why i'm asking. all i did was: 0.34^(1/2) - (0.85)^(1/3)

Answer 9

You're applying my 3rd formula wrong. Maybe I typed it ambiguously.

a * log(b) = log(b^a)

Answer 10

right*

Answer 11

So how did you apply that to\[\log(x^\frac{1}{2})\]

Answer 12

you are treating them like
\[(log_{b}x)^{1/2}\]
instead of what they actually are:
\[log_{b}(x^{1/2})\]

Answer 13

oh so would it be log(0.34)^(1/2) - log(0.85)^(1/3)???

Answer 14

No. You need to do the manipulation before trying to plug in the actual values. Did you get to a point where you had a term like\[\log(x^{1/2})\]

Answer 15

um yes..

Answer 16

Use dmacine's 3rd formula rule thing before you use the actual values of log x and log y.

Answer 17

And after you applied the identity log(b^a) = a log(b) what did you get?

Answer 18

You can use it to turn the exponent into a multiply. You just move that exponent out front. So now apply that operation to\[\log(x^{1/2})\]