What is 4log_{10}(x-3)-2log_{10}(1-2x) ?

The solution to 4log_{10}(x-3)-2log_{10}(1-2x) is log_{10}(((x-3)^4)/((1-2x)^2))

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simplify 4log_{10}(x-3)-2log_{10}(1-2x)

simplify

4 lo g_{10} (x - 3) - 2 lo g_{10} (1 - 2 x)

lo g_{10} (\frac{( x - 3 ) ^{4}}{( 1 - 2 x ) ^{2}})

Solution steps

4 lo g_{10} (x - 3) - 2 lo g_{10} (1 - 2 x)

Apply log rule:

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

4 lo g_{10} (x - 3) = lo g_{10} ((x - 3)^{4})

= lo g_{10} ((x - 3)^{4}) - 2 lo g_{10} (- 2 x + 1)

Apply log rule:

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

2 lo g_{10} (- 2 x + 1) = lo g_{10} ((- 2 x + 1)^{2})

= lo g_{10} ((x - 3)^{4}) - lo g_{10} ((- 2 x + 1)^{2})

Apply log rule:

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

lo g_{10} ((x - 3)^{4}) - lo g_{10} ((1 - 2 x)^{2}) = lo g_{10} (\frac{( x - 3 ) ^{4}}{( - 2 x + 1 ) ^{2}})

= lo g_{10} (\frac{( x - 3 ) ^{4}}{( 1 - 2 x ) ^{2}})

ln (4 x^{2} - 5) - ln (x^{2})

ln (\frac{45}{75})

\frac{1}{i} (ln (2.414 - 0.011 i) - ln (2.054 - 0.0423 i))

lo g_{10} (x) - \frac{1}{2} lo g_{10} (x^{2} + 8)

ln (\frac{5}{15})

What is 4log_{10}(x-3)-2log_{10}(1-2x) ?
The solution to 4log_{10}(x-3)-2log_{10}(1-2x) is log_{10}(((x-3)^4)/((1-2x)^2))