Using laws of logarithms write the expression below as a sin

Using laws of logarithms, write the expression below as a single logarithm.

Using laws of logarithms, write the expression below using sums and/or differences of logarithmic expressions which do not contain the logarithms of products, quotients, or powers.

Solution

ln x^2 - ln (x+3)

using log properties

ln a - ln b = ln (a/b)

ln x^2 - ln (x+3) = ln ( x^2 / (x+3))

ln ( x(10-x )^4 )

ln (a*b ) = ln a + ln b

ln (a^y) = y ln a

therefore , ln ( x(10-x )^4 ) = ln x + ln (10-x)^4

= ln x + 4 ln (10-x)

3) ln (x) = -1

using log property

y = ln x

x = e^y

therefore ,

ln (x) = -1

x = e^-1

4) log (x+3) = 4

applying log property

log x = y

x = 10^y

therefore,

log (x+3) = 4

(x+3) = 10^4

x = 10^4 - 3