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

lnx² - ln(x-3) = ln x^2 - ln x + ln 3

= 2 ln x - ln x + ln 3

= ln x + ln 3

= ln (3x)

ln(9x⁸ ) + ln(8x⁵ ) = ln ( 9x⁸ *8x⁵) = ln ( 72x¹³)

ln (x(10-x)⁴ ) = ln x + 4 ln (10-x) = ln x + 9.2 - 4lnx = 9.2 - 3 ln x

log(x+3) = 4

e^log(x+3) = e⁴

(x+3) = e^4

ln(x) = -1

e^ln x = e^-1

^{x = e^-1}

ln (16) = x²

e^ln16 = e^x2

16 = e^x2