What is log_{10}((-2^7)/(\sqrt[3]{-9^712^5)}) ?

The solution to log_{10}((-2^7)/(\sqrt[3]{-9^712^5)}) is log_{10}(-128)-1/3 log_{10}(-3^{19}*1024)

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simplify log_{10}((-2^7)/(\sqrt[3]{-9^712^5)})

simplify

lo g_{10} (- 128) - \frac{1}{3} lo g_{10} (- 3^{19} \cdot 1024)

Solution steps

Apply log rule:

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

= lo g_{10} (- 2^{7}) - \frac{1}{3} lo g_{10} (- 3^{19} \cdot 4^{5})

2^{7} = 128

= lo g_{10} (- 128) - \frac{1}{3} lo g_{10} (- 3^{19} \cdot 4^{5})

4^{5} = 1024

= lo g_{10} (- 128) - \frac{1}{3} lo g_{10} (- 3^{19} \cdot 1024)

lo g_{6} (\frac{2}{9 z})

\frac{1}{2} ln (x) + \frac{1}{2} ln (y)

lo g_{10} (14) + \frac{1}{2} lo g_{10} (3) - lo g_{10} (2)

lo g_{5} (a^{2} + 10 a + 9) - lo g_{5} (a + 9) + 2

lo g_{10} (7.2) - lo g_{10} (6.7)

What is log_{10}((-2^7)/(\sqrt[3]{-9^712^5)}) ?
The solution to log_{10}((-2^7)/(\sqrt[3]{-9^712^5)}) is log_{10}(-128)-1/3 log_{10}(-3^{19}*1024)