If the function fx-log1-ax-log1-bxx- x- 0 is continuous at x-0 then- f0-

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Question

If the function $f (x) = \frac{l o g (1 + a x) - l o g (1 - b x)}{x}, x \neq 0$ is continuous at $x = 0$ then, $f (0) =$ ________.

l o g a - l o g b

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a + b

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l o g a + l o g b

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a - b

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f (x) = \frac{log (1 + a x) - log (1 - b x)}{x}

x \neq 0

x = 0

f (0) =

a, b > 0, a, b \neq 1, c > 0

{log}_{a} c = \frac{{log}_{b} c}{{log}_{b} a} = ({log}_{b} c) ({log}_{a} b)

{log}_{\sqrt{2}} x + 2 {log}_{2} x + {log}_{1 / 2} x = 9

f (x) = \frac{l o g (1 + a x) - l o g (1 - b x)}{x}

f (x) = \{\begin{cases} \frac{\log (1 + a x) - \log (1 - b x)}{x}, & x \neq 0 \\ k, & x = 0 \end{cases}

f (x) = \frac{log (1 + a x) - l o g (1 - b x)}{x}

x \neq 0

f (0) = k

f (x)

x = 0

k

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