What is ln(((-288*10^9))/(x^2)) ?

The solution to ln(((-288*10^9))/(x^2)) is ln(288)+9ln(10)-2ln(x)

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simplify ln(((-288*10^9))/(x^2))

simplify

ln (\frac{( - 288 \cdot 1 0 ^{9} )}{x ^{2}})

ln (288) + 9 ln (10) - 2 ln (x)

Solution steps

ln (\frac{( - 288 \cdot 1 0 ^{9} )}{x ^{2}})

Apply log rule:

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

ln (\frac{( - 288 \cdot 1 0 ^{9} )}{x ^{2}}) = ln ((- 288 \cdot 1 0^{9})) - ln (x^{2})

= ln (- 1 0^{9} \cdot 288) - ln (x^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{2}) = 2 ln (x)

= ln (- 288 \cdot 1 0^{9}) - 2 ln (x)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (- 288 \cdot 1 0^{9}) = ln (288) + ln (1 0^{9})

= ln (288) + ln (1 0^{9}) - 2 ln (x)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (1 0^{9}) = 9 ln (10)

= ln (288) + 9 ln (10) - 2 ln (x)

lo g_{a} (x) + lo g_{a} (y) - lo g_{a} (t)

ln (11 x) - ln (11)

8 lo g_{8} (6 x)

lo g_{10} (x) + 5 lo g_{10} (y) - 3 lo g_{10} (z)

ln (5 π)

What is ln(((-288*10^9))/(x^2)) ?
The solution to ln(((-288*10^9))/(x^2)) is ln(288)+9ln(10)-2ln(x)