What is log_{4}(16x^4)-log_{4}((2x)^2) ?

The solution to log_{4}(16x^4)-log_{4}((2x)^2) is log_{4}(4x^2)

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simplify log_{4}(16x^4)-log_{4}((2x)^2)

simplify

lo g_{4} (16 x^{4}) - lo g_{4} ((2 x)^{2})

lo g_{4} (4 x^{2})

Solution steps

lo g_{4} (16 x^{4}) - lo g_{4} ((2 x)^{2})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{4} (16 x^{4}) - lo g_{4} ((2 x)^{2}) = lo g_{4} (\frac{16 x ^{4}}{( 2 x ) ^{2}})

= lo g_{4} (\frac{16 x ^{4}}{( 2 x ) ^{2}})

Cancel

\frac{16 x ^{4}}{( 2 x ) ^{2}} : 4 x^{2}

= lo g_{4} (4 x^{2})

- lo g_{10} (7.2 \cdot 1 0^{- 7})

3 ln (2) + \frac{1}{3} ln (8) - \frac{1}{2} ln (25)

2 ln (t) + 5 ln (z) - ln (t)

lo g_{10} (\frac{85347 x ^{15274}}{125386})

- lo g_{10} (1.74 \times 1 0^{- 5})

What is log_{4}(16x^4)-log_{4}((2x)^2) ?
The solution to log_{4}(16x^4)-log_{4}((2x)^2) is log_{4}(4x^2)