Question

For the following equation,

log(6.9-y) - log(y) = log(1.1+x4) - 5log(x)

Express y explicitly as a function of x. Hence, determine the value of y when x = 3.4, giving your answer to 3 decimal places.

Answer 1

so using log laws

\[\log(6.9-y)-\log(y) = \log(1.1 + x^4) - 5\log(x)\]

\[\log{((6.9-y)/y)} = \log((1.1 + x^4)/x^5) \]

\[\log(6.9/y - y/y) = \log(1.1/x^5 + x^4/x^5)\]

find the exponent of each side

\[6.9/y - 1 = 1.1x^{-5} + x^{-1}\]

take the reciprocal of both sides

\[y/6.9 - 1 = x^5/1.1 - x\]

\[y = 6.9(x^5/1.1 + x + 1)\]

Answer 2

I'll let you do the substitution of 3.4 to find y

Answer 3

thanks for your help!

Answer 4

log(6,9-y)/y =log(1,1 +x^4)/x^5 so than
(6,9-y)/y =(1,1 +x^4)/x^5
x^5(6,9-y)=y(1,1 +x^4)
6,9x^5 -yx^5 =y(1,1 +x^4)
6,9x^5 =y(1,1 +x^4)+yx^5
6,9x^5 =y(1,1 +x^4 +x^5)

y=(6,9x^5)/(1,1 +x^4 +x^5)

when x=3,4
so than

y=(6,9(3,4)^5)/(1,1 +(3,4)^4 +(3,4)^5) =(6,9(454,354))/(1,1 +133,633 +454,354)=
=3135,044/589,087 =5,321

3,4^4 = 133,633
3,4^5 =454,354

so the answer wann to be 5,321

Answer 5

cambell_st, i think your answer is wrong.. i tried and manage to get the same answer as jhonyy