The value of the determinantloga x-y logay-z loga z-x logby-z logb z-x logb x-y logc z-x logc x-y logc y-z is

Log_n m =ln m/ln n Δ = log_a (x/y ) amp; log_a(y/z ) amp; log_a (z/x ) log_b(y/z ) amp;log_b (z/x ) amp;log_b (x/y ) log_c (z/x ) amp; log ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Evaluation of a Determinant

The value of ...

Question

The value of the determinant
$∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} l o g_{a} (\frac{x}{y}) & l o g_{a} (\frac{y}{z}) & l o g_{a} (\frac{z}{x}) l o g_{b} (\frac{y}{z}) & l o g_{b} (\frac{z}{x}) & l o g_{b} (\frac{x}{y}) l o g_{c} (\frac{z}{x}) & l o g_{c} (\frac{x}{y}) & l o g_{c} (\frac{y}{z}) \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣$ is

$l o g_{a} (x y z) + l o g_{b} (x y z) + l o g_{c} (x y z)$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$a l o g_{e} x + b l o g_{e} y + c l o g_{e} z$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

-1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

Suggest Corrections

Similar questions

∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} l o g_{a} (\frac{x}{y}) & l o g_{a} (\frac{y}{z}) & l o g_{a} (\frac{z}{x}) l o g_{b} (\frac{y}{z}) & l o g_{b} (\frac{z}{x}) & l o g_{b} (\frac{x}{y}) l o g_{c} (\frac{z}{x}) & l o g_{c} (\frac{x}{y}) & l o g_{c} (\frac{y}{z}) \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ ∣ \begin{matrix} l o g_{a} (x / y) & l o g_{a} (y / z) & l o g_{a} (z / x) l o g_{b} (y / z) & l o g_{b} (z / x) & l o g_{b} (x / y) l o g_{c} (z / x) & l o g_{c} (x / y) & l o g_{c} (y / z) \end{matrix} ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} {log}_{a} (\frac{x}{y}) & {log}_{a} (\frac{y}{z}) & {log}_{a} (\frac{z}{x}) {log}_{b} (\frac{y}{z}) & {log}_{b} (\frac{z}{x}) & {log}_{b} (\frac{x}{y}) {log}_{c} (\frac{z}{x}) & {log}_{c} (\frac{x}{y}) & {log}_{c} (\frac{y}{z}) \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣

| z - 1 | + | z |

| z | + | z - 1 | + | z - 2 |

Join BYJU'S Learning Program