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LaronJaxon
Group Title
What is the solution to the equation 1/sqrt 8= 4^(m  3) ?
 one year ago
 one year ago
LaronJaxon Group Title
What is the solution to the equation 1/sqrt 8= 4^(m  3) ?
 one year ago
 one year ago

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

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
One 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
 one year ago

terenzreignz Group TitleBest 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...
 one year ago

terenzreignz Group TitleBest 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 \[\huge 2^{2(m3)}=2^{2m  6}\]
 one year ago

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

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