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I am learning about natural logarithms and this is the first equation i must solve:

$$ 30 - 23 e^{-0.027x} > 20 $$

Could somebody explain what i should do to solve this and other equations like these? Thanks

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  • $\begingroup$ The function $\ln$ (or $\log$ depending on how you write the natural logarithm) is the inverse of the function $\exp$. $\endgroup$ – mvw Feb 23 '15 at 14:06
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Hint:

Move the constant to right:

$$-23e^{-0.027x}>-10$$

Divide with $-23$:

$$e^{-0.027x}<\frac{10}{23}$$

And now! You can soon get the log of both sides!

$$\log{e^{-0.027x}}<\log{\frac{10}{23}}$$

Good luck! And learn at least basic equation solving, without them all of such problems will be much harder!

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  • $\begingroup$ log or ln ? If base is not mentioned log means to the base 10 $\endgroup$ – Vikram Feb 23 '15 at 14:20
  • $\begingroup$ @Vikram I learned $\ln{}$ as the natural logarithm in the basic school, but everywhere on the net I found this as $\log{}$. I think the $\ln{}$ would be better, but I must adapt the convention. $\endgroup$ – peterh Feb 23 '15 at 14:22

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