The equation \(16 \cdot 4^{-x} = 4^x - 6\) can be solved by first multiplying both sides by \(4^x\), leading to the quadratic form \(16 = (4^x)^2 - 6 \cdot 4^x\). By substituting \(u = 4^x\), the equation simplifies to a standard quadratic equation, which can be solved for \(u\). The final solution for \(x\) is obtained using the formula \(x = \frac{\ln u}{\ln 4}\). This method effectively resolves the equation without the need for logarithmic manipulation at the outset.
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Petrus said:Hello MHB,
I am stuck on this equation and don't know what to do, If i take ln it does not work, any advice?
$$16•4^{-x}=4^x-6$$
Regards,
$$|\pi\rangle$$