You are Here: Home >< Maths

C1 quick q watch

1. 81^x + 81 = 30(9^x)

Find the value of x.
2. (Original post by The Chameleon)
81^x + 81 = 30(9^x)

Find the value of x.

can you confirm the 30 in the question, please?
3. substitute for u=9^x
4. 81^x = (9^2)^x = 9^2x
u=9^x
u^2 + 81 = 30u
So.. solve u^2 - 30u + 81 = 0
(u + 27)(u + 3) = 0
u = -27 or -3

Then substitute the u back.
5. (Original post by Fermat)
substitute for u=9^x
81^x + 81 = 30(9^x)

Like Fermat said. Make it into a quadratic with u=9^x

so (9^x)^2+81-30(9^x)=0
u^2-30u+81=0
(u-15)^2+81-225=0
so (u-15)^2=144
u-15=±12
so u=3 or 27

so either 9^x=3,
3^(2x)=3
so 2x=1, so x=1/2

or 9^x=27
so 3^(2x)=3^3
so 2x=3, so x=3/2
6. Ok... ignore mine
7. my teacher taught me this method.. i'm not sure if it's right or not:

81^x + 81 = 30(9^x)

(3^4)^x + (3^4)^1 = 30(3^2)^x
as 3 is a common, you can substitute y in for it instead
so you get y^4x + y = 30y^2
y^4x - 30y^2x + y = 0
something is wrong in my arithmetic there, but that's the method

4x+ 4 = 60x
4x=56
x=14
[also answer may be wrong, but method of substitution is right. hope that helps
8. (Original post by The Chameleon)
81^x + 81 = 30(9^x)

Find the value of x.
81^x + 81 = 30(9^x)
(9^x)^2 - 30*(9^x) + 81 = 0
(9^x - 27)(9^x - 3) = 0
9^x = 27 or 9^x = 3
x = 3/2 or 1/2

yeah others got the same Im glad to see
9. (Original post by mik1a)
81^x + 81 = 30(9^x)
(9^x)^2 - 30*(9^x) + 81 = 0
(9^x - 27)(9^x - 3) = 0
9^x = 27 or 9^x = 3
x = 3/2 or 1/2

yeah others got the same Im glad to see
Can someone explain this to me?

Wouldn't (9^x)^2 give 81^2x whereas we are given 81^x?
10. (Original post by The Chameleon)
Can someone explain this to me?

Wouldn't (9^x)^2 give 81^2x whereas we are given 81^x?
no

(9^x)^2=9^x.9^x
=9^(2x)
=(9^2)^x
=81^x
11. 81 is the same as 9^2

=> 81^x = (9^2)^x.

When indicies are like that we multiply them together

=> (9^2)^x = 9^2x

However, it doesn't matter which way round we multiply them, it will still yield the same answer. So,

=> (9^2)^x = (9^x)^2

This second form is more useful as it allows you to substitue in for u=9^x on both sides of the equation.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: December 28, 2004
Today on TSR

Here's what to do next...

University open days

• University of East Anglia
All Departments Open 13:00-17:00. Find out more about our diverse range of subject areas and career progression in the Arts & Humanities, Social Sciences, Medicine & Health Sciences, and the Sciences. Postgraduate
Wed, 30 Jan '19
• Solent University
Sat, 2 Feb '19
• Sheffield Hallam University
Sun, 3 Feb '19
Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants