Question

condense the expression: 1/2Log5 16-3log5 x+4Log5y

Answer 1

first move the coefficients that are infront of the logarithms to the right

Answer 2

meaning log\[\log_{5} 16^{1/2}\]

Answer 3

ignore the first log my equations button is not working

Answer 4

but the log expression below is correct use that example to simplify the other two

Answer 5

then let me know what you got

Answer 6

log5y^x+4?

Answer 7

\[\log_{5} 4-\log_{5} x ^{3}+\log_{5} y ^{4}\]

Answer 8

thankyou for helping me their just really hard for me ;(

Answer 9

no problem

Answer 10

have time for more?

Answer 11

we aren't done yet sorry, now when you are subtract two logs with the same base do you condense them by multiplying them together or dividing them?

Answer 12

dividing

Answer 13

yes so log base 4 is on top the numerator making the other two...?

Answer 14

on the bottom being multiplied together

Answer 15

idk

Answer 16

because they were being added

Answer 17

so can you show me what your answer would be?

Answer 18

4/x^3+y^4

Answer 19

when you are adding two logs together with the same base then you multiply them together

Answer 20

okay

Answer 21

\[\log_{5} (4/x ^{3}y ^{4})\]

Answer 22

does that make sense

Answer 23

yes

Answer 24

i just want to make sure you understand rather than just giving you the answer so that later you can ace a test on this if you need to

Answer 25

yah this good

Answer 26

ok why we try another problem. this will be the last one i can help with, then i have to go alright?

Answer 27

okay

Answer 28

solve the equation; 15+2 log2 x=31

Answer 29

so when solving for any variable the whole point is to get the variable by itself so what would be one thing we can move away from the side with x easily?

Answer 30

yes

Answer 31

that was a question

Answer 32

and the answer is 15

Answer 33

woudnt it be 17?

Answer 34

i didn't mean the final answer, i meant that it will be easy to move the fifteen since the fifteen is not attached to anything

Answer 35

move to be 15

Answer 36

yes we subtract fifteen from both sides then we simplify the logarithm but first what does the new equation look like?

Answer 37

it will equeal 16instead of 31

Answer 38

yes

Answer 39

know we focus on the log

Answer 40

;)

Answer 41

okay!

Answer 42

what can we move to condense the logarithm more?

Answer 43

the 2 in front

Answer 44

yes

Answer 45

ah yes!!

Answer 46

so what do we have now?

Answer 47

logx=16

Answer 48

no... \[\log_{2} x ^{2}=16\]

Answer 49

does that make sense?

Answer 50

yes

Answer 51

okay a trick that i learned is you put the same base of the log you want to remove under both sides of the equation like so: \[2^{\log_{2}x ^{2} }=2^{16}\]

Answer 52

now what can you simplify?

Answer 53

exponents

Answer 54

yes \[x ^{2}=2^{16}\] is our new equation as 2^log base 2 equals one

Answer 55

now what would be the next step?

Answer 56

logx=4

Answer 57

why would we do that when we already have x by itself.
what we would do is simplify 2^16=65536

Answer 58

then x^2=65536

Answer 59

65536?

Answer 60

yes now what would you do to get x all by itself?

Answer 61

take the root of x and the other side

Answer 62

x=256

Answer 63

does that make sense?

Answer 64

thats what i thought

Answer 65

\[\sqrt{x ^{2}}=\sqrt{65536}=x=256\]

Answer 66

omg thankyou so much

Answer 67

no problem I have to go now, but i wish you the best of luck :)

Answer 68

thankyou