What is log_{10}((-2^7)/(\sqrt[3]{-9^7*12^5)}) ?

The solution to log_{10}((-2^7)/(\sqrt[3]{-9^7*12^5)}) is log_{10}(-128)-1/3 log_{10}(-3^{19}*1024)

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simplify log_{10}((-2^7)/(\sqrt[3]{-9^7*12^5)})

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)

ln (2 (3 x - 2 y)) \cdot 8

lo g_{5} (\frac{125}{x + 5})

ln (\frac{1 - a x}{2})

lo g_{2} (\frac{5}{50})

lo g_{10} (\frac{4 x ^{3}}{y ( x - 2 ) ^{6}})

What is log_{10}((-2^7)/(\sqrt[3]{-9^7*12^5)}) ?
The solution to log_{10}((-2^7)/(\sqrt[3]{-9^7*12^5)}) is log_{10}(-128)-1/3 log_{10}(-3^{19}*1024)