What is log_{10}(7)-log_{10}(1/49) ?

The solution to log_{10}(7)-log_{10}(1/49) is 3log_{10}(7)

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simplify log_{10}(7)-log_{10}(1/49)

simplify

lo g_{10} (7) - lo g_{10} (\frac{1}{49})

3 lo g_{10} (7)

Decimal Notation

2.53529 \dots

Solution steps

lo g_{10} (7) - lo g_{10} (\frac{1}{49})

Apply log rule:

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

lo g_{10} (7) - lo g_{10} (\frac{1}{49}) = lo g_{10} (\frac{7}{\frac{1}{49}})

= lo g_{10} (\frac{7}{\frac{1}{49}})

\frac{7}{\frac{1}{49}} = 343

= lo g_{10} (343)

Factor the number:

343 = 7^{3}

= lo g_{10} (7^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{10} (7^{3}) = 3 lo g_{10} (7)

= 3 lo g_{10} (7)

lo g_{8} (3) + lo g_{8} (x^{3} - 2) + lo g_{8} (2)

lo g_{10} (\frac{4 ( x + 6 ) ^{5}}{x ^{3}})

ln (\frac{1}{9 ^{k}})

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

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

What is log_{10}(7)-log_{10}(1/49) ?
The solution to log_{10}(7)-log_{10}(1/49) is 3log_{10}(7)