if f(x)=ln(2x + 3), solve for f(x + h) - f(x - h)

asked by guest
on Jan 09, 2025 at 10:15 pm



You asked:

Evaluate the function \(f\left( x \right) = \ln\left( 2 x + 3 \right)\), \(f\left( x + h \right) - f\left( x - h \right)\).

MathBot Answer:

$$\begin{aligned}f\left( x + h \right) - f\left( x - h \right)&=- \log{\left(- 2 h + 2 x + 3 \right)} + \log{\left(2 h + 2 x + 3 \right)}\end{aligned}$$

$$\begin{aligned}f\left( x + h \right) - f\left( x - h \right)&=- \log{\left(3 + 2 \left(- h + x\right) \right)} + \log{\left(3 + 2 \left(h + x\right) \right)}\\f\left( x + h \right) - f\left( x - h \right)&=- \log{\left(- 2 h + 2 x + 3 \right)} + \log{\left(2 h + 2 x + 3 \right)}\\\end{aligned}$$

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