Question

Solve the given equation
Please help
Equation is in comments

Answer 1

To solve exponential equations like these the base on both sides of the = sign must be the same. In the equation
2401^(2n) = 343^(n+2),
the base on the left is 2401 and on the right is 343.

Can you think of a number which when multiplied with itself many times gives you 343 and also when multiplied with itself more number of times it gives 2401 ?

Answer 2

It would have to be something near 18.54

Answer 3

7^3 = 343 and 7^4 = 2401

Answer 4

So the common base on both sides can be changed to 7

Answer 5

oh ok so i have to find the common base of the two and then what

Answer 6

it's better to use 343 as the common base....

Answer 7

like navk said, take log with base 343 on both sides

Answer 8

True, but the equation can directly be solved without using logs, so that would prove simpler

Answer 9

Can you explain this one problem step by step for me and then I should be able to do the rest by myself

Answer 10

First convert both the sides of the equation to base 7 using 7^3 = 343 and 7^4 = 2401 like this:

\[(7^4)^{2n} = (7^3)^{n+2}\]
Now simplify further by multiplying the exponents:

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

When bases on both sides are same, that is 7, then exponents are same as well. So you get

8n = 3n + 6
5n = 6
n = 6/5

Answer 11

Do you understand @shelbygt520

Answer 12

Awesome yes thank you so much @navk

Answer 13

Hey Jess it's been a while

Answer 14

ikr :D

Answer 15

What are you up to these days XD