Question

1296^2n=216^n+10

Answer 1

can someone please help me!

Answer 2

solve for n given 1296^2n=216^n+10

Answer 3

hello SOS means someone help me i need help someone please

Answer 4

well is the question

\[1296^{2n} = 216^{n + 10}\]

Answer 5

yes

Answer 6

First notice that 1296 and 216 are both powers of 6:

\[\Large 6^4 = 1296\]
\[\Large 6^3 = 216\]

Answer 7

ok... write your questions with the sme base

1296 = 6^4

and

216 = 6^3

so you are now solving

\[(6^4)^{2n} = (6^3)^{n + 10}\]

use the power of a power law

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

you have

\[6^{8n} = 6^{3n + 30}\]

same base just equate the powers and solve for n

8n = 3n + 30

hope this helps

Answer 8

yes so what do i do first

Answer 9

do i move 3n over

Answer 10

subtract 3n from both sides as the 1st step

Answer 11

Do you understand how to get it to 8n = 3n + 30 ?

Answer 12

ie the steps campbell_st took to get it to that point.

Answer 13

ok i see so it would be 5n=30 right and divide by 5?

Answer 14

is the answer 6?
thanks

Answer 15

yes thats the answer.

Answer 16

thank you can you help me on solving this 24012n=343^n+2

Answer 17

i mean help on 2401^2n=343^n+2

Answer 18

\[\Large 2401^{2n}=343^{n+2}\]

\[\Large 7^4 = 2401\]
\[\Large 7^3 = 343\]

So you have
\[\LARGE (7^4)^{2n}=(7^3)^{n+2}\]

Now use the same rule as above \[\Large (x ^a)^b = x^{a \times b}\]

Answer 19

so would it be 7^8n=7^3n+2?

Answer 20

help

Answer 21

Almost.. but you forgot to distribute the 3.

\[\LARGE 7^{4 \times 2n}=7^{3\times (n+2)}\]

Answer 22

so it would be 7^8n=7^3n+6?

Answer 23

still there?

Answer 24

what do i do next?

Answer 25

:( help......PLEASE

Answer 26

HELP Iam stilll HERE

Answer 27

anyone HELP

Answer 28

Gosh at least can i get the answer if U dont want to explain

Answer 29

fine

Answer 30

agentOsmith thank you and can u finish what u started

Answer 31

campbell_st can you help me

Answer 32

what is 6.5% growth in decimal

Answer 33

Slow down, i'm helping you figure out the answer.

so it would be 7^8n=7^3n+6?

is correct.

\[\Large 7^{8n}=7^{3n+6}\]

Now since the bases are the same (the base is the 7), you can equate the exponents (the powers on the 7) and solve for n.

Answer 34

so 7^5n=7^6

Answer 35

Well you just want to equate the exponents, you want to drop the 7's entirely.

Answer 36

so 7^6=11n?

Answer 37

If \[\Large x^a = x^b\]
then \[\Large a = b\]

\[\Large 7^{8n}=7^{3n+6}\]
so...

Answer 38

7=11n+6

Answer 39

\[\Large 7^{(8n)}=7^{(3n+6)} \]
the stuff in the brackets on the left, must be equal to the stuff in the brackets on the right.

Answer 40

so is it 8n=3n+6

Answer 41

so is it 6/5

Answer 42

what about 2^x+4 =2^2x+5

Answer 43

6/5 is right.

\[\Large 2^{(x+4)} =2^{(2x+5)}\]

Again, the stuff in the brackets must be equal, since the bases (the 2) are the same.

Answer 44

so x+4=2x+5 therefor the answer is -1

Answer 45

Correct.

Answer 46

thank you for your help and for being patient

Answer 47

i love this website

Answer 48

No prob, but a medal would be nice :P