Logarithim Help.

hobbes

hobbes

Member
If "Log a B = c^4" and "Log b A = 5/c^3" prove that c= 1/5

lower case letters are suppsoed to be subscripts and the "^" sign is exponet and the "/" is a fraction sign.

Any help would be great.
 
it's definitley Advanced Math 12, which is a step up from grade 12 adcademic math but I am taking it in grade 11 to take pre- cal next year.
 
If "Log a B = c^4" and "Log b A = 5/c^3" prove that c= 1/5

Use antilogs. If Log a B = C^4 then a^(C^4) = B, and for Log b A = 5/(C^3), b^(5/(C^3)) = A, solve from there.
 
Log a B = C^4 --> B = A * C^4

Log b A = 5/C^3 --> A = B * 5/C^3

Sub in "B*5/C^3" for A --> B = B * 5/C^3 * C^4

C's cancel --> B = B * 5 * C

Divide both sides by 5B (B's cancel) --> 1/5 = C
 
Since log a b = c^4, a^(c^4) = b. So, a = b^(1/c^4). So, bringing the other equation into the mix, we get:

b^(1/c^4) = b^(5/c^3)

So, 1/c^4 = 5/c^3 and 1/5 = c^4/c^3. Cancel on the right side and you get:

1/5 = c.

thankyouverymuch
 
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