Solve ln32c^350d1d

Evaluate

ln (32 c^{3} \times 50 d \times 1 \times d)

Multiply the terms

More Steps

ln (1600 c^{3} d^{2})

Use lo g_{a} (x \times y) = lo g_{a} (x) + lo g_{a} (y) to transform the expression

ln (1600) + ln (c^{3}) + ln (d^{2})

Simplify the expression

More Steps

2 ln (40) + ln (c^{3}) + ln (d^{2})

Use lo g_{a} b^{n} = n lo g_{a} b to simplify the expression

2 ln (40) + 3 ln (c) + ln (d^{2})

Solution

2 ln (40) + 3 ln (c) + 2 ln (d)

Expand the expression