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:

engeline says

this is good

John kaluba says

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

stephen says

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

j says

how would you solve this if ^ means to the power of-

2^(x)3^(y)=6

j hate says

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

lope says

how would you solve this if ^ means to the power of-

(2^2x+1)9^x=6^x

Anon says

wow this is really helpful, thank you soo much!

can someone help me with this? please

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

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)

alake says

x5=125*squreroot of 2 pls solve d equation

Tharindu says

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

katherine says

write in the form of a power of m/n

?(ab-1)

Angelealendo says

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

rajarshi says

solve for x and y

x^x+y^y=31

x^y+y^x=17

Maaaryam says

This is so helpful:)

Dwight says

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

Oluwabukunmi says

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

Maxi says

Can sumone plz solve dis Indices for me.

Simplyfy -10a^2b^3[(-5a)^2/3b-1/3]

Lil legend says

.Cn sum1 help me wit dix plx

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

rahim says

pls solve X^2=16^X for me

Ai Ling says

May I know which grade you are?

Praveen says

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.

Comments and sharing are welcome.

Cheers

Praveen says

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.

Shila says

Help on this

(81^2)*×(27^*)÷(9^*)=729

Where * represents the unknown

Paul Amegadze says

Would like a help on

X^2= 16^x

Thanks