Question

how can we solve log base 64 of x+log base8 of x+log base 2 of x=18?

Answer 1

\[\log_{64} X+\log_{8}X +\log_{2}X =18\]
is that right ?

Answer 2

yes

Answer 3

ok ,so do u know from where do we start ?

Answer 4

no idea

Answer 5

ok first lets start with the rule with is :
\[\log_{a}X = \log_{\sqrt{a}} \sqrt{X} = \log_{a^2} X^2\]

Answer 6

do u know this rule ?

Answer 7

yeah saw it

Answer 8

Do u know now from where we can start ?

Answer 9

change the base or something?

Answer 10

thats right ,In order to make all the bases the same so we can collect them ..
lets start with \[\log_{64}X \] change it to the base 2 ,can u do it ?

Answer 11

2^6?

Answer 12

thats awesome right but we will use the root in order to reduce it so it will be\[\log_{64}X = \log_{\sqrt[6]{64}} \sqrt[6]{X}=\log_{2} \sqrt[6]{X}\]

Answer 13

you got it ?

Answer 14

8?

Answer 15

lets move to \[\log_{8}X \]---> what can u do here ?

Answer 16

3/2
0r 2^3?

Answer 17

So we will use the cubic root in order to reduce it to two so it will be \[\log_{8}X =\log_{\sqrt[3]{8}} \sqrt[3]{X} = \log_{2} \sqrt[3]{?}\]

Answer 18

sry instead of ? put X

Answer 19

okay

Answer 20

no we got all the bases equal ,so what rule we gonna use now ?

Answer 21

can we add them?

Answer 22

now *

Answer 23

we will use the rule\[\log_{a} M + \log_{a} N = \log_{a} M \times N\] ,Do u know this rule >?

Answer 24

yeah

Answer 25

good so lets now collect them ,but first do u know how to convert a root into a power ?

Answer 26

yes

Answer 27

are you there?

Answer 28

still need help?

Answer 29

yes