Question

if x²+y²=z²,then log base y(z+x)+log base y(z-x)?
wt is the ans?​

Answer 1

Explanation:

Given :-

x²+y² = z²

To find :-

Find the value of log base y(z+x)+log base y(z-x) ?

Solution :-

Given that

x²+y² = z²

=> y² = z²-x² -----------(1)

Now,

log base y(z+x)+log base y(z-x)

=> log base y (z+x)(z-x)

Since log ab = log a + log b

=> log base y ( z²-x²)

Since (a+b)(a-b) = a²-b²

=> log base y (y²)

Since from (1)

=> 2 log base y (y)

Since log a^m = m log a

=> 2×1

Since log base a (a) = 1

=> 2

Answer:-

The value of log base y(z+x)+log base y(z-x) is 2

Used formulae:-

→ log ab = log a + log b

→ (a+b)(a-b) = a²-b²

→ log a^m = m log a

→ log base a (a) = 1