0
$\begingroup$

I need to find $x$ from this equation: $$4^{x+1} + 4^{1-x} = 10$$

Since this is an addition and not multiplication, I cannot add the exponents. I do recognise that I will most likely have to use logarithms to solve this, but I cannot figure out how to manipulate the equation. I tried taking logs of both sides and writing it all in terms of base $4$ but that did not help.

Any help on how to solve for $x$?

$\endgroup$
1
$\begingroup$

Write your equation in the form $$4\cdot 4^x+\frac{4}{4^x}=10$$ and substitute $$t=4^x$$, now solve the quadratic.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.