How to solve a logarithm?

Question

I'm stumble upon the following logarithm expression. What is the value of $x$ in it? $$\log_x (x^5) = 5$$

For any $x\in(0,1)\cup(1,\infty)$ the equality holds. – Ángel Mario Gallegos Mar 15 '17 at 02:53 — Ángel Mario Gallegos, Mar 15 '17 at 02:53
Anything but 1, at 1 we divide by 0 – Teh Rod Mar 15 '17 at 02:55 — Teh Rod, Mar 15 '17 at 02:55

score 1 · Accepted Answer · answered Mar 15 '17 at 02:54

1

HINT:

By definition, $y=\log_b(a)$ if $a=b^y$ for $b\ne 1$.

Here, we have $b=x$, $y=x$, and $a=x^5$.

What can you conclude now?

answered Mar 15 '17 at 02:54

Mark Viola

Then it'll be X^5 = X^5. Both will cancel out. So 1=1. – gmail user Mar 15 '17 at 02:59
Actually, $x^5=x^5$ for all $x$. However, we need to have $x^5>0$ and $x\ne 1$. And that is that. ;-)) – Mark Viola Mar 15 '17 at 03:02
Still no clue. How do I get x here? – gmail user Mar 15 '17 at 03:04
1

$x$ can be any non-negative number except for $1$. – Mark Viola Mar 15 '17 at 03:05

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