Question

if x3 + y3=0 x+y is not equal to zero then log(x+y)=​

Answer 1

Question :

if $\tt {x}^{3} + {y}^{3}$ =0 , x + y ≠ 0 then log(x+y)=

Solution :

We know that

$\tt {(x+y)}^{3} = {x}^{3} +{y}^{3} +3xy(x+y)$

$\tt \implies {(x+y)}^{3} = 0 + 3xy(x+y)$

$\tt \implies {(x+y)}^{3} = 3xy(x+y)$

$\tt \implies {(x+y)}^{2} = 3xy$

Taking log on both sides

$\tt \implies log{(x+y)}^{2} = log(3xy)$

$\tt \implies 2log(x+y) = log(3xy)$

$\tt \implies log(x+y) = \frac{1}{2}log(3xy)$

$\tt \therefore log(x+y) = \frac{1}{2}log(3xy)$

Properties of log

● $\tt {log}_{a}{bc} = {log}_{a}{b} + {log}_{a}{c}$

● $\tt {log}_{a}{\frac{b}{c}} = {log}_{a}{b} - {log}_{a}{c}$

● $\tt {log}_{a}{a} = 1$

●$\tt {log}_{a}{1} = 0$

●$\tt {log}_{a}{{b}^{c}} = c{log}_{a}{b}$

Answer 2

$\large\blue{QUESTION}$

if x³+y³ = 0 , x+y≠0 , find log ( x + y)

ANSWER

• x³+y³ = 0

• (x+y) ( x² - xy + y²) = 0

since x+y ≠0 , it can be neglected equation changes to ,

• x² - xy + y² = 0

• x² + y² = xy (xy is brought to right side)

adding a 2xy on LHS and RHS,

• x² + y² + 2xy = 3xy

• (x+y)² = 3 xy

• x+y = (3xy) ^(1/2) ( √3 can be written as 3^(1/2))

applying log on both sides,

• log(x +y ) = 1/2 log ( 3xy )

= 1/2( log 3 + log x + log y )