Question

Prove that
prove this
​

Answer 1

To prove :

$\sf log_{y}( {x}^{2} ). log_{z}( {y}^{3} ) .log_{x}( {z}^{5} ) = 30$

Proof :

LHS =

$\sf log_{y}( {x}^{2} ). log_{z}( {y}^{3} ) .log_{x}( {z}^{5} )$

use logarithms rule,

$\boxed{\sf log_{a} {m}^{n} = n log_{a}m}$

therefore,

$\sf = 2 log_{y}x \times 3 log_{z}y \times 5 log_{x}z$

$=\sf 30 log_{y}x . log_{z}y. log_{x}z$

we know,

$\boxed{ \sf log_{b}m = \frac{ log_{a}m }{ log_{a}b}}$

therefore,

$\sf= 30 \times \frac{logx}{logy} \times \frac{logy}{logz} \times \frac{logz}{logx}$

$\sf = 30$

= RHS

Hence proved.

Answer 2

Answer:

Step-by-step explanation:

㏒y x² * ㏒z y³ * logx z^5=2*3*5=10