What is 4log_{10}(x+5)-log_{10}(2-x) ?

The solution to 4log_{10}(x+5)-log_{10}(2-x) is log_{10}(((x+5)^4)/(2-x))

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simplify 4log_{10}(x+5)-log_{10}(2-x)

simplify

4 lo g_{10} (x + 5) - lo g_{10} (2 - x)

lo g_{10} (\frac{( x + 5 ) ^{4}}{2 - x})

Solution steps

4 lo g_{10} (x + 5) - lo g_{10} (2 - x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 lo g_{10} (x + 5) = lo g_{10} ((x + 5)^{4})

= lo g_{10} ((x + 5)^{4}) - lo g_{10} (- x + 2)

Apply log rule:

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

lo g_{10} ((x + 5)^{4}) - lo g_{10} (2 - x) = lo g_{10} (\frac{( x + 5 ) ^{4}}{- x + 2})

= lo g_{10} (\frac{( x + 5 ) ^{4}}{2 - x})

(ln (2) + 1.76274 + ln (3)) \cdot \frac{π}{16}

\frac{1}{4} \cdot ln (\frac{( x + 1 )}{x - 1})

3 + lo g_{10} (\frac{0.7 - x}{x})

lo g_{2} ((x^{3} + 2) (x - 9)^{3})

n \cdot (35.2 \cdot ln (\frac{420}{293}) - 8.314 \cdot ln (\frac{2500}{500}))

What is 4log_{10}(x+5)-log_{10}(2-x) ?
The solution to 4log_{10}(x+5)-log_{10}(2-x) is log_{10}(((x+5)^4)/(2-x))