What is log_{10}(6.5x10^7)-log_{10}(1000) ?

The solution to log_{10}(6.5x10^7)-log_{10}(1000) is 3+log_{10}(65x)

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simplify log_{10}(6.5x10^7)-log_{10}(1000)

simplify

lo g_{10} (6.5 x 1 0^{7}) - lo g_{10} (1000)

3 + lo g_{10} (65 x)

Solution steps

lo g_{10} (6.5 x \cdot 1 0^{7}) - lo g_{10} (1000)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (6.5 x \cdot 1 0^{7}) - lo g_{10} (1000) = lo g_{10} (\frac{6.5 x \cdot 1 0 ^{7}}{1000})

= lo g_{10} (\frac{6.5 x \cdot 1 0 ^{7}}{1000})

Cancel

\frac{6.5 x \cdot 1 0 ^{7}}{1000} : 65000 x

= lo g_{10} (65000 x)

Apply log rule:

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

lo g_{10} (65000 x) = lo g_{10} (65000) + lo g_{10} (x)

= lo g_{10} (65000) + lo g_{10} (x)

lo g_{10} (65000) = 3 + lo g_{10} (65)

= 3 + lo g_{10} (65) + lo g_{10} (x)

Apply log rule:

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

lo g_{10} (65) + lo g_{10} (x) = lo g_{10} (65 x)

= 3 + lo g_{10} (65 x)

\frac{1}{2} ln (\frac{e + e ^{2} - 1}{e - e ^{2} - 1})

6 \cdot ln (3) - 6 \cdot ln (2)

\frac{10000}{200 π ^{2}} (ln (\frac{400}{0.4}) + ln (8))

6 ln (2 (0 + 1))

\frac{e ^{\frac{7}{4}}}{4} + ln (\frac{e ^{\frac{7}{4}}}{2})

What is log_{10}(6.5x10^7)-log_{10}(1000) ?
The solution to log_{10}(6.5x10^7)-log_{10}(1000) is 3+log_{10}(65x)