What is 800ln(10)-480ln(6)-320 ?

The solution to 800ln(10)-480ln(6)-320 is 384000ln((5^{800}*2^{320})/(3^{480)})-320

Popular >

simplify 800ln(10)-480ln(6)-320

simplify

800 ln (10) - 480 ln (6) - 320

384000 ln (\frac{5 ^{800} \cdot 2 ^{320}}{3 ^{480}}) - 320

Solution steps

800 ln (10) - 480 ln (6) - 320

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (10) - ln (6) = ln (\frac{10}{6})

= 800 \cdot 480 ln (\frac{10}{6}) - 320

\frac{1 0 ^{800}}{6 ^{480}} = \frac{5 ^{800} \cdot 2 ^{320}}{3 ^{480}}

= 800 ln (\frac{5 ^{800} \cdot 2 ^{320}}{3 ^{480}}) \cdot 480 - 320

Multiply the numbers:

800 \cdot 480 = 384000

= 384000 ln (\frac{5 ^{800} \cdot 2 ^{320}}{3 ^{480}}) - 320

\frac{1}{2} lo g_{2} (3) - 2 lo g_{2} (5)

lo g_{10} (\frac{x ^{5}}{y ^{3}})

lo g_{2} (\frac{8}{x + 4})

lo g_{2} (x) - lo g_{2} (x^{8})

3 \cdot lo g_{2} (p) + 7 \cdot lo g_{2} (q)

What is 800ln(10)-480ln(6)-320 ?
The solution to 800ln(10)-480ln(6)-320 is 384000ln((5^{800}*2^{320})/(3^{480)})-320