Question

4 power x +6 power x=9 power x
Ans plz

Answer 1

Step-by-step explanation:

Given

4 power x +6 power x=9 power x Ans plz

So the equation is 4^x + 6^x = 9^x

We can write the given equation as  

               (2^x)^2 + 2^x 3^x = (3^x)^2

Dividing both sides by (3^x)^2 we get

         ((2/3)^x)^2 + (2/3)^x = 1

Let a = (2/3)^x  

we get  a^2 + a – 1 = 0

This is a quadratic equation, so we get

    So x = - b + - √b^2 – 4ac / 2a

    So x = - 1 + - √1^2 – 4(1) (-1) / 2 (1)

    So x = - 1 + - √5 /2

 Now (2/3)^x = -1 + √5 / 2 ( positive root)

So x = log – 1 + √5 / 2 / log 2/3

        = log (√5 – 1) – log 2 / log 2 – log 3

So x = 1.1868

Answer 2

Hope it helps

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