hexaedru8p

2022-09-06

Condense the expression to the logarithm of a single quanity.

$${\mathrm{log}}_{7}(5x)-8{\mathrm{log}}_{7}(x)$$

$${\mathrm{log}}_{7}(5x)-8{\mathrm{log}}_{7}(x)$$

Elisa Spears

Beginner2022-09-07Added 9 answers

Answer:

$${\mathrm{log}}_{7}(5x)-8{\mathrm{log}}_{7}(x)\phantom{\rule{0ex}{0ex}}\Rightarrow {\mathrm{log}}_{7}5x{\mathrm{log}}_{7}(8x{)}^{8}\phantom{\rule{0ex}{0ex}}\Rightarrow {\mathrm{log}}_{7}5x-{\mathrm{log}}_{7}{x}^{8}\phantom{\rule{0ex}{0ex}}\Rightarrow {\mathrm{log}}_{7}\frac{5x}{{x}^{7}}\phantom{\rule{0ex}{0ex}}\Rightarrow {\mathrm{log}}_{7}\frac{5}{{x}^{7}}$$

$${\mathrm{log}}_{7}(5x)-8{\mathrm{log}}_{7}(x)\phantom{\rule{0ex}{0ex}}\Rightarrow {\mathrm{log}}_{7}5x{\mathrm{log}}_{7}(8x{)}^{8}\phantom{\rule{0ex}{0ex}}\Rightarrow {\mathrm{log}}_{7}5x-{\mathrm{log}}_{7}{x}^{8}\phantom{\rule{0ex}{0ex}}\Rightarrow {\mathrm{log}}_{7}\frac{5x}{{x}^{7}}\phantom{\rule{0ex}{0ex}}\Rightarrow {\mathrm{log}}_{7}\frac{5}{{x}^{7}}$$

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