How do you solve $5^{x} = 20$ $5^x= 20$ ?

Question

How do you solve $5^{x} = 20$ $5^x= 20$ ?

1 Answer

Impact of this question

1659 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-06T08:19:52

Take logs and use properties of logs to find:

$x = \frac{log 20}{log 5} = \frac{1 + log 2}{1 - log 2} \approx 1.86135$ $x = (log 20)/(log 5) = (1+log 2)/(1 - log 2) ~~ 1.86135$

Explanation:

If we take common logs of both sides then we get:

$log 20 = {log 5}^{x} = x log 5$ $log 20 = log 5^x = x log 5$

So $x = \frac{log 20}{log 5}$ $x = (log 20)/(log 5)$

We can do a little more with this if we know the log value $log 2 \approx 0.30103$ $log 2 ~~ 0.30103$ and that $log 10 = 1$ $log 10 = 1$ :

$log 5 = log (\frac{10}{2}) = log 10 - log 2 = 1 - log 2$ $log 5 = log (10/2) = log 10 - log 2 = 1 - log 2$

$\approx 1 - 0.30103 = 0.69897$ $~~ 1 - 0.30103 = 0.69897$

$log 20 = log (10 \cdot 2) = log 10 + log 2 = 1 + log 2$ $log 20 = log (10*2) = log 10 + log 2 = 1 + log 2$

$\approx 1 + 0.30103 = 1.30103$ $~~ 1 + 0.30103 = 1.30103$

So $x = \frac{log 20}{log 5} \approx \frac{1.30103}{0.69897} \approx 1.86135$ $x = (log 20)/(log 5) ~~ 1.30103 / 0.69897 ~~ 1.86135$

Science

Math

Humanities

... and beyond

How do you solve $5^{x} = 20$ $5^x= 20$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve 5x=205^x= 20?

1 Answer

Explanation:

Related questions

Impact of this question

How do you solve $5^{x} = 20$ $5^x= 20$ ?