Question

Log and fractions?↓↓↓↓↓↓↓↓

Answer 1

please help

Answer 2

1) put the exponents inside the logs, using

\(\LARGE\color{blue}{ \bf a~log(b)=log(b^A) }\)


2) Use \(\LARGE\color{blue}{ \bf log(c)+log(v) =log(c \times v) }\)

Then you will see that you can remove the \(\LARGE\color{blue}{ \bf log_7 }\) from everywhere.

Answer 3

what would b and a be?

Answer 4

i have a question
do you know what \(\large 64^{\frac{1}{3}}\) is?

Answer 5

Like 64 times 1/3 or 193/3?

Answer 6

yeah, i had a feeling that was going to be the problem

Answer 7

\[\large 64^{\frac{1}{3}}\neq 64\times \frac{1}{3}\]

Answer 8

\[\large 64^{\frac{1}{3}}=\sqrt[3]{64}\]

Answer 9

in english, the cubed root of 64
do you know what that number is?

Answer 10

4?

Answer 11

right
so let me write out one first step for you
using as @SolomonZelman said
\[\huge n\log(x)=\log(x^n)\] you have
\[\huge \frac{1}{3}\log(64)=\log(64^{\frac{1}{3}})=\log(4)\] clear?

Answer 12

k so now just do the same to the other one but the square root?

Answer 13

right!
let me know what you get, because there is one more step after that

Answer 14

\[\log(4)+\log(11)=\log(x) \]

Answer 15

ok good
now only two more steps, and the last one is really nothing
using
\[\log(A)+\log(B)=\log(A\times B)\] what do you get on the left hand side of the equal sign ?

Answer 16

\[\log(4)+\log(11)\]

Answer 17

that is what you have
make it look like
\[\log(A\times B)\] now

Answer 18

log(4*11)=log(44)

Answer 19

got it!

Answer 20

Thank you!

Answer 21

and now the last nothing step
if
\[\log(44)=\log(x)\] the guess what \(x\) is?

Answer 22

44

Answer 23

bingo
hope the steps were more or less clear

Answer 24

Yes very clear thanks!

Answer 25

yw