What is log_{10}(12+1/2)log_{10}(7)-log_{10}(2) ?

The solution to log_{10}(12+1/2)log_{10}(7)-log_{10}(2) is log_{10}((7^{log_{10}(25/2)})/2)

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simplify log_{10}(12+1/2)log_{10}(7)-log_{10}(2)

simplify

lo g_{10} (12 + \frac{1}{2}) lo g_{10} (7) - lo g_{10} (2)

lo g_{10} (\frac{7 ^{l o g_{10} (\frac{25}{2})}}{2})

Decimal Notation

0.62596 \dots

Solution steps

lo g_{10} (12 + \frac{1}{2}) lo g_{10} (7) - lo g_{10} (2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

lo g_{10} (7) lo g_{10} (\frac{1}{2} + 12) = lo g_{10} (7^{l o g_{10} (\frac{1}{2} + 12)})

= lo g_{10} (7^{l o g_{10} (\frac{1}{2} + 12)}) - lo g_{10} (2)

Apply log rule:

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

lo g_{10} (7^{l o g_{10} (12 + \frac{1}{2})}) - lo g_{10} (2) = lo g_{10} (\frac{7 ^{l o g_{10} (\frac{1}{2} + 12)}}{2})

= lo g_{10} (\frac{7 ^{l o g_{10} (12 + \frac{1}{2})}}{2})

7^{l o g_{10} (12 + \frac{1}{2})} = 7^{l o g_{10} (\frac{25}{2})}

= lo g_{10} (\frac{7 ^{l o g_{10} (\frac{25}{2})}}{2})

110 (ln (24) - ln (19)) + 55

5 ln (\cdot 5 l^{2})

2 lo g_{10} (\frac{5}{4})

\frac{1}{2} ln (\frac{4 3 + 6}{3})

ln (\frac{1.1 \cdot 1 0 ^{6}}{1.2 \cdot 1 0 ^{3}})

What is log_{10}(12+1/2)log_{10}(7)-log_{10}(2) ?
The solution to log_{10}(12+1/2)log_{10}(7)-log_{10}(2) is log_{10}((7^{log_{10}(25/2)})/2)