Question

Find the value of 1/logx(yz)+1/logy(zx)+1 + 1/logz(xy)+1

Answer 1

Answer:

1

Step-by-step explanation:

Given  

Find the value of 1/logx(yz)+1/logy(zx)+1 + 1/logz(xy)+1

We know that log a(b) = log b / log a and log a + log b + log c = log (abc)

Now 1/log x(yz) + 1/log y(xz) + 1/log z(xy)

= 1 / (log (yz) / log x + 1 ) + 1 / (log (zx) / log y + 1 + 1 / log (xy) / log z + 1

= 1 / (log yz + log x) / log x + 1 / (log zx + log y) / log y + 1 / (log xy + log z) / log z)

= 1 / log (xyz)  / log x + 1/ log (xyz) / log y + 1/log (xyz) / log z)

= log x / log (xyz) + logy / log(xyz) + log z / log (xyz)

= (log x + log y + log z) / log (xyz)

= log (xyz) / log (xyz)

= 1

Answer 2

Answer:

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