Simplify the following: 1_8(x) - 1_7(x) + 1_6(x) - 1_5(x) + 1_4(x) - 1_3(x) + 1_2(x) Option 1: _8 (16x/35) Option 2: _2 (5x/2) Option 3: _x (128/35) Option 4: _x (1/40320)

The answer is '_x (128/35)'. View full solution:

Modern Math > Logarithms

Medium

Simplify the following: $\dfrac{1}{\log_{8}(x)} - \dfrac{1}{\log_{7}(x)} + \dfrac{1}{\log_{6}(x)} - \dfrac{1}{\log_{5}(x)} + \dfrac{1}{\log_{4}(x)} - \dfrac{1}{\log_{3}(x)} + \dfrac{1}{\log_{2}(x)}$

$\log_{8} (\frac{16x}{35})$

$\log_{2} (\frac{5x}{2})$

$\log_{x} (\frac{128}{35})$

$\log_{x} (\frac{1}{40320})$

✅ Correct Option: 3