How do you solve $ln x + ln 5 = ln10$ ?

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Answer 1 · 2015-11-29T18:13:50

$x=2$

Subtract $ln(5)$ from both sides:

$ln(x) = ln(10)-ln(5)$

Use the rule $ln(a)-ln(b)=ln(a/b)$ :

$ln(x)=ln(10/5)=ln(2)$ .

Since the logarithm is injective, $x$ must be $2$ . If you want to see it in an other way, take the exponential on both sides:

$e^{ln(x)} = e^{ln(2)}$

Since logarithm and exponential are inverse functions, we have that $e^{ln(z)}=z$ . So,

$x=2$

How do you solve ln x + ln 5 = ln10ln x + ln 5 = ln10?