Question

expand the following .


1)log 1000

2) log(128/625)

3) log x²y³z4 (it is z to the power 4)

4) log p² q³ / r

5) log √x³/y²

Answer 1

1) log 1000 = log 10³ = 3log10

2) $log \frac{128}{625} = log 128 - log 625$
    ⇒ $log 2^7 - log 5^4 = 7log 2 - 4 log 5$

3) log x²y³z^4 = log x² + logy³ + logz^4
    ⇒ 2logx + 3logy + 4logz

4)  log p²q³/r = log p² + logq³ - logr = 2log p + 3log q - logr

5) $log \sqrt{ \frac{x^3}{y^2}} = log (\frac{x^3}{y^2}) ^ \frac{1}{2}$

⇒1/2[ log x³ - logy²]

⇒ 1/2 [ 3logx - 2logy]

Answer 2

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..