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

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

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

malice
 8 months ago
Best ResponseYou've already chosen the best response.0The answer is m=9/4 (just took the test and got it right)
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