Some help with Indices!

WhiskeyGoblin

Have a few repeats and one of my biggest problems across 2 of the exams (Differential Calc and Intergral Calc) is indices! Cutting through assignments atm and have come across a problem I just haven't a clue how to do! Would appreciate any help if possible!


Problem:


[latex]\left(\frac{1}{5} \right)^2^x = 625 [/latex]



Cant get the code quite right but it's supposed to read to the power of 2x


Thanks in advance!


Mark

Yakuza

[latex]\left({\frac{1}{5}}\right)^{2x} = 625 = 5^4[/latex]

This is the same as [latex]5^{-2x} = 5^4[/latex]

What happens if you take the log in base 5 of both sides? Remember that [latex] log_n (n^a) = a[/latex]

TheBody

Yakuza wrote: »

[latex]\left({\frac{1}{5}}\right)^{2x} = 625 = 5^4[/latex]

This is the same as [latex]5^{-2x} = 5^4[/latex]

What happens if you take the log in base 5 of both sides? Remember that [latex] log_n (n^a) = a[/latex]

Or even just compare both sides.

Yakuza

Indeed, but the OP mentioned he was having issues with indices, so I thought a refresher would be apt.

WhiskeyGoblin

Thanks for the help! Kinda get it now :P