How do I convert this into a quadratic?

Question

aravindg · Answer

$$5^{x - 1} + 5(0.2)^{x-2} = 26 $$

hartnn · Answer

is the equation correct ? verify again...

aravindg · Answer

Yes it is right. You can verify it: 3 and 1 are the roots.

parthkohli · Answer

Knowing that makes things easier.

**If** this is a quadratic, then it has two roots at max.  You know what they are... so it can be written in the form $a(x-1)(x-3)$.  Let's see what $a$ is.

hartnn · Answer

its not at all a quadratic equation, its an exponential equation (and i think it cannot be converted to quadratic)
its has 2 real roots, and 2 complex roots

hartnn · Answer

***many (infinite) complex roots

parthkohli · Answer

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

hartnn · Answer

which topic does this question belong ?

aravindg · Answer

So how am I supposed to find the real roots for such an equation? Trial and error?

hartnn · Answer

trial and error can easily lead you to x=1
but x=3 ....

aravindg · Answer

...

parthkohli · Answer

$$(x-1) \log(5)+5(x-2)\log(5)=\log(26)$$$$(x-1 + 5(x-2))=\dfrac{\log(26)}{\log(5)}$$

parthkohli · Answer

Hmm wait, that's 0.2

aravindg · Answer

:O

parthkohli · Answer

Then it's 5^(-1)

aravindg · Answer

Who taught you log(a+b)=log a+log b?

hartnn · Answer

^

parthkohli · Answer

No, I raised that to the power 5 instead of 0.2.

hartnn · Answer

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