Can someone explain to me how I would go about doing this? (problem posted below)

I think I need to combine log and 11^x somehow, like 11^log[3] for example.

Question

Can someone explain to me how I would go about doing this? (problem posted below)

I think I need to combine log and 11^x somehow, like 11^log[3] for example.

anonymous · Answer

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zepdrix · Answer

Buhaha what a weird problem XD
Thinking...

anonymous · Answer

Interesting!!! @mathmale @dan815

zepdrix · Answer

Oh oh I have an idea.
Recall that we can rewrite a value like this $\Large\rm x=e^{\ln x}$.

Let's try to apply that to our problem here,$$\LARGE\rm \color{orangered}{5^{1.3}}=11^{\log_{11}(\color{orangered}{5^{1.3}})}$$

zepdrix · Answer

Let's deal with what's in the exponent for a sec,

zepdrix · Answer

Our exponent rule give sus,$$\Large\rm 1.3 \log_{11}5$$Then change of base will get it done I think!!
Let's see...

zepdrix · Answer

$$\Large\rm 1.3 \frac{\log_3 5}{\log_{3}11}$$

zepdrix · Answer

$$\LARGE\rm \color{orangered}{5^{1.3}}=11^{\left(\Large\rm 1.3 \frac{\log_3 5}{\log_{3}11}\right)}$$

zepdrix · Answer

That should work, yes? :D
That only uses 11^x, multiplication, and log base 3.

anonymous · Answer

Oh my gosh, you're right! It's complicated, but it works :'D thank you so much!

zepdrix · Answer

yay \c:/
fun problem!!