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terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1\[\large \frac{1}{\sqrt{8}}=4^{m3}\]

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1One nifty way of doing this is to try to express both sides of the equation as exponentials, ie, one base, one exponent... preferably with the same base. So, let's start with \[\frac{1}{\sqrt{8}}\] 8 is just 2³, so let's put it that way...\[\large \frac{1}{\sqrt{2^{3}}}\] And remember that taking the square root means raising something to the 1/2 power, so...\[\huge \frac{1}{\left( 2^3 \right)^{\frac{1}{2}}}\] Using laws of exponents, you get

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1\[\huge \frac{1}{2^{\frac{3}{2}}}\]Now remember that \[\large a^{n}=\frac{1}{a^n}\] So eventually, we're left with \[\huge \frac{1}{\sqrt{8}} = 2^{\frac{3}{2}}\] Now on to the other side of the equation...

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1\[\large 4^{m3}\] But 4 = 2² So, we can write it as \[\huge (2^2)^{m3}\] Again, using laws of exponents, it is just equal to \[\huge 2^{2(m3)}=2^{2m  6}\]

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1So, your problem becomes... \[\huge 2^{\frac{3}{2}}=2^{2m  6}\] Which can only mean \[\large \frac{3}{2}=2m  6\]

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1And the rest, is history :D
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