What is ln(1/(a+b*x/d+c*(x/d)^g)) ?

The solution to ln(1/(a+b*x/d+c*(x/d)^g)) is -ln((bx)/d+c(x/d)^g+a)

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simplify ln(1/(a+bx/d+c(x/d)^g))

simplify

ln (\frac{1}{a + b \cdot \frac{x}{d} + c \cdot ( \frac{x}{d} ) ^{g}})

- ln (\frac{b x}{d} + c (\frac{x}{d})^{g} + a)

Solution steps

ln (\frac{1}{a + b \frac{x}{d} + c ( \frac{x}{d} ) ^{g}})

Apply log rule:

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

ln (\frac{1}{a + b \frac{x}{d} + c ( \frac{x}{d} ) ^{g}}) = ln (1) - ln (a + b \frac{x}{d} + c (\frac{x}{d})^{g})

= ln (1) - ln (b \frac{x}{d} + c (\frac{x}{d})^{g} + a)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (b \frac{x}{d} + c (\frac{x}{d})^{g} + a)

Multiply

b \frac{x}{d} : \frac{b x}{d}

= 0 - ln (\frac{b x}{d} + c (\frac{x}{d})^{g} + a)

0 - ln (a + \frac{x b}{d} + c (\frac{x}{d})^{g}) = - ln (a + \frac{x b}{d} + c (\frac{x}{d})^{g})

= - ln (\frac{b x}{d} + c (\frac{x}{d})^{g} + a)

ln (a + b) - ln (a^{2} - b^{2}) + 2 ln (c)

3 lo g_{10} (2) + 4 lo g_{10} (x)

5 lo g_{a} (x) - 7 lo g_{a} (y^{6})

lo g_{4} (\frac{1}{4} x^{2} y)

3 ln (2) + 2 ln (x) - \frac{1}{2} \cdot ln (x + 3)

What is ln(1/(a+b*x/d+c*(x/d)^g)) ?
The solution to ln(1/(a+b*x/d+c*(x/d)^g)) is -ln((bx)/d+c(x/d)^g+a)