What is log_{10}(10xsqrt(x-3)) ?

The solution to log_{10}(10xsqrt(x-3)) is 1+log_{10}(x)+log_{10}(sqrt(x-3))

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simplify log_{10}(10xsqrt(x-3))

simplify

lo g_{10} (10 x x - 3)

1 + lo g_{10} (x) + lo g_{10} (x - 3)

Solution steps

lo g_{10} (10 x x - 3)

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{10} (10 x x - 3) = lo g_{10} (10) + lo g_{10} (x x - 3)

= lo g_{10} (10) + lo g_{10} (x x - 3)

Apply log rule:

lo g_{a} (a) = 1

lo g_{10} (10) = 1

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

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{10} (x x - 3) = lo g_{10} (x) + lo g_{10} (x - 3)

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

Apply rule:

a + (b + c) = a + b + c

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

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

lo g_{6} (216 x)

- 4 ln (x) - 2 ln (y) - 3 ln (z)

lo g_{5} (\frac{25 b ^{5} y ^{2} - 9}{y ( x + 9 ) ^{2}})

ln (7) + ln (4)

ln (\frac{83}{3})

What is log_{10}(10xsqrt(x-3)) ?
The solution to log_{10}(10xsqrt(x-3)) is 1+log_{10}(x)+log_{10}(sqrt(x-3))