# A-Math: Solving Indices Equation (Involving Common Base)

This topic is taught in Secondary 3 after introduction of Indices Law.

In solving indices equation involving the same base, one of the common techniques is by Substitution. But before you can do substitution, you need to apply indices law to 'break down' the equation. This process of breaking down is sometimes challenging for students. Knowing how to solve quadratic equation is also essential.

Sometimes, solving Indices Equation will also involve the concept of taking lg on both sides as well.

In the following example, you will Substitution and 'Breaking down' in action:

### Ai Ling Ong

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### 24 Responses to A-Math: Solving Indices Equation (Involving Common Base)

1. John kaluba says:

You are such a great Mathematics. Iam impressed with your method of solving complex equations

2. Yes you deserve a big up congratulation.Mathematics is no longer turf subject!

3. j says:

how would you solve this if ^ means to the power of-
2^(x)3^(y)=6

with 2 unknowns you need 2 equations to solve for the unknowns

4. lope says:

how would you solve this if ^ means to the power of-
(2^2x+1)9^x=6^x

5. Anon says:

wow this is really helpful, thank you soo much!

can someone help me with this? please

4^p-3 * 7^q-1 ?

6. lpo says:

no root exist

Possible derivation:
d/dp(4^(p-3) 7^(q-1))
| Factor out constants:
= | 7^(q-1) (d/dp(4^(p-3)))
| Use the chain rule, d/dp(4^(p-3)) = ( d4^u)/( du) ( du)/( dp), where u = p-3 and ( d4^u)/( du) = 4^u log(4):
= | 7^(q-1) (4^(p-3) log(4) (d/dp(p-3)))
| Differentiate the sum term by term:
= | 4^(p-3) 7^(q-1) log(4) (d/dp(p)+d/dp(-3))
| The derivative of -3 is zero:
= | 4^(p-3) 7^(q-1) log(4) (d/dp(p)+0)
| The derivative of p is 1:
= | 1 4^(p-3) 7^(q-1) log(4)

7. alake says:

x5=125*squreroot of 2 pls solve d equation

8. Tharindu says:

x^(x+1)+x^(2-x)-5^3-1=0

9. katherine says:

write in the form of a power of m/n

?(ab-1)

10. Angelealendo says:

Can someone help me with this: show that (8x^2)^8-r (1/2x)=2^24-4r(X^16-3r)

11. rajarshi says:

solve for x and y
x^x+y^y=31
x^y+y^x=17

Sounds and looks complicated but actually not too bad once we see the trick. Maybe the qn should include the additional stipulation that x and y are integers.

Then, by simple trial and error, x and y are 2 and 3 (Either way).

Nice qn.

12. Maaaryam says:

13. Dwight says:

I got lost at the quadratic equation it's not clear how you got (y-9)(y+1)=0

14. Oluwabukunmi says:

Solve for:3^2y_6(3^y)=27

15. Maxi says:

Can sumone plz solve dis Indices for me.
Simplyfy -10a^2b^3[(-5a)^2/3b-1/3]

16. Lil legend says:

.Cn sum1 help me wit dix plx

4/25^-1/2, multiply by 2^4 divid by (15/2^-2.

17. rahim says:

pls solve X^2=16^X for me

May I know which grade you are?

Interesting qn Rahim.

The answer is -0.5 I believe. You can either use graphing calculator or 'trial and error' method. I don't think you can do such questions using conventional logarithmic techniques.

If the qn were slightly modified, example x^2=3^x, and you are not allowed to use graphing calculator, then may need to rely on more advanced techniques such as Newton-Raphson method.

Cheers

18. Shila says:

Help on this
(81^2)*×(27^*)÷(9^*)=729

Where * represents the unknown