What is expand log_{10}(log_{10}(10000^{25x})) ?

The solution to expand log_{10}(log_{10}(10000^{25x})) is 2log_{10}(5)+log_{10}(x)+2log_{10}(2)

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Popular >

expand log_{10}(log_{10}(10000^{25x}))

expand

lo g_{10} (lo g_{10} (1000 0^{25 x}))

2 lo g_{10} (5) + lo g_{10} (x) + 2 lo g_{10} (2)

Solution steps

lo g_{10} (lo g_{10} (1000 0^{25 x}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} (1000 0^{25 x}) = 25 x lo g_{10} (10000)

= lo g_{10} (25 x lo g_{10} (10000))

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (25 x lo g_{10} (10000)) = lo g_{10} (25) + lo g_{10} (x) + lo g_{10} (lo g_{10} (10000))

= lo g_{10} (25 lo g_{10} (10000) x)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (25 x lo g_{10} (10000)) = lo g_{10} (25) + lo g_{10} (x) + lo g_{10} (lo g_{10} (10000))

= lo g_{10} (25) + lo g_{10} (x) + lo g_{10} (lo g_{10} (10000))

lo g_{10} (25) = 2 lo g_{10} (5)

lo g_{10} (lo g_{10} (10000)) = 2 lo g_{10} (2)

= 2 lo g_{10} (5) + lo g_{10} (x) + 2 lo g_{10} (2)

ln (3 x + 1) - ln (x + 2)

lo g_{3} (\frac{ab}{c d})

lo g_{10} (rs)

ln (\frac{x ^{2} y ^{3}}{w ^{4} z ^{5}})

ln (\frac{1 + 1}{x})

What is expand log_{10}(log_{10}(10000^{25x})) ?
The solution to expand log_{10}(log_{10}(10000^{25x})) is 2log_{10}(5)+log_{10}(x)+2log_{10}(2)