Expand the logarithm into a sum or difference of logs with no exponents:

Question

show step by step work:

ln(125e²(x²y)³)

Answer 1

= ln125 + lne^2 + ln((x^2y)^3)

= ln5^3 + 2lne + 3ln(x^2y)

= 3ln5 +2(1) + 3(lnx^2) +3lny

= 3ln5 +2 +6lnx +3lny

Answer 2

ln(125e²(x²y)³)=ln(125) + ln(e²) + ln(x⁶)+ln(y³)

= ln(5³) + 2(1) + 6ln(x)+ 3ln(y)

= 3ln(5)+2 + 6ln(x) + 3ln(y)

Answer 3

ln(125e²(x²y)³) = ln 125 + ln e² + ln (x² y )³

= ln 5³ + 2 ln e + 3 ln (x² y )

= 3 ln 5 + 2 *1 + 3( ln x² + ln y)

= 3 ln5 +2 + 3 ln x² + 3 ln y

= 3 ln 5 + 2 + 3*2 ln x + 3 ln y

= 3 ln 5 +2 +6 ln x +3 ln y

Answer 4

ln(125e²(x²y)³)

First, simplify the exponents:

ln(5³·e²·x⁶·y³)

Now apply the log property log(a·b) = log(a) + log(b)

ln(5³·e²·x⁶·y³) = ln(5³) + ln(e²) + ln(x⁶) + ln(y³)

Now apply the log property log(a^b) = b·log(a)

ln(5³) + ln(e²⁾ + ln(x⁶) + ln(y³) = 3·ln(5) + 2·ln(e) + 6·ln(x) + 3·ln(y)

Finally, note that ln(e) = 1:

3·ln(5) + 2 + 6·ln(x) + 3·ln(y)