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Can someone explain including working out how to solve this?

$$\dfrac{5^x}{x} = 79.85957$$

I know that the answer is $x = 3.5$, but how does one normalise the equation so that the x is on one side?

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    This is called a [transcendental equation](http://en.wikipedia.org/wiki/Transcendental_equation). They are solved by approximations only.2012-08-22
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    @KarolisJuodelė There's no evidence that *each* transcendental equation could not be solved out *explicitly*. And we should point out what is *explicit*, say, the finite composition of addition, subtraction, multiplying, division and take logarithm, take exponent, and a list of constants (e.g. $1$, $i$, $\pi$, $e$, $\gamma$).2012-08-22
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    Notice the equation $e^x=3$ has no explicit solution in terms of algebraic operations (this excludes the logarithm). However, once we invent the log function then we have an *explicit* solution $\ln 3$. What exactly constitutes an *explicit* solution depends on the universe of allowed functions. Apparently, if we include the Lambert W function then there is an explicit solution. With this understanding the distinction between solving $e^x=3$ and the $5^x/x=79$ is removed. You can argue the natural log is more natural! But, others argue to include Lambert in our lexicon of basic functions.2012-08-22

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