Question

Expand the following.
(i) log1000 (ii) log (128/625) (iii) logx²y³z⁴
(iv) log (p²q³/r) (v) log √(x³/y²)

Answer 1

SOLUTION :

1) log 1000

= log 10³  

[By power law :log a (mⁿ) = n (log a m) ]

= 3log10

log 1000 = 3log10

2) log 128/625  

= log 128 - log 625

[By quotient law :log a (m/n) = log a m - log a n ]

= log 2^7 - log 5⁴

= 7log2 - 4log5

[By power law :log a (mⁿ) = n (log a m) ]

log 128/625 = 7log2 - 4log5

3) log x²y³z⁴

= log x² + logy³ + logz⁴

[By product law :log a (mn) = log a m + log a n ]

= 2logx + 3logy + 4logz

[By power law :log a (mⁿ) = n (log a m) ]

log x²y³z⁴ = 2logx + 3logy + 4logz

4)  log p²q³/r

= log p² + logq³ - logr

[By product & quotient law]

= 2log p + 3log q - logr

[By power law]

log p²q³/r = 2log p + 3log q - logr

5) log√x³/y²

= log (x³/y²)^1/2

= 1/2[ log x³ - logy²]

[By quotient law]

= 1/2 [ 3logx - 2logy]

[By power law]

log√x³/y² = 1/2 [ 3logx - 2logy]

HOPE THIS ANSWER WILL HELP YOU..

Answer 2

Hi ,

*******************************************

We know the Logarithmic rules:

i ) log mn = log m + log n

ii ) log(m/n ) = log m - log n

iii ) log mⁿ = n log m

************************************************

i ) log ( 1000 )

= log ( 2³ × 5³ )

= log 2³ + log 5³

= 3 log 2 + 3 log 5

ii ) log ( 128/625 )

= log 128 - log 625

= log 2^7 - log 5⁴

= 7 log 2 - 4 log 5

iii ) log ( x²y³z⁴ )

= log x² + log y³ + log z⁴

= 2 log x + 3 log y + 4 log z

iv ) log ( p²q³/r )

= log ( p²q3 ) - log r

= log p² + log q³ - log r

= 2 log p + 3 log q - log r

v ) log√( x³/y² )

= log ( x³/y² )^½

= 1/2 [ log ( x³/y² )

= 1/2 [ log x³ -log y² ]

= 1/2 [ 3 log x - 2 log y ]

=( 3/2)log x - log y

I hope this helps you.

: )