What is simplify-25log_{10}(3)+25log_{10}(7) ?

The solution to simplify-25log_{10}(3)+25log_{10}(7) is 25log_{10}(7/3)

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simplify-25log_{10}(3)+25log_{10}(7)

simplify

- 25 lo g_{10} (3) + 25 lo g_{10} (7)

25 lo g_{10} (\frac{7}{3})

Decimal Notation

9.19941 \dots

Solution steps

- 25 lo g_{10} (3) + 25 lo g_{10} (7)

Apply log rule:

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

25 lo g_{10} (3) = lo g_{10} (3^{25})

= - lo g_{10} (3^{25}) + 25 lo g_{10} (7)

Apply log rule:

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

25 lo g_{10} (7) = lo g_{10} (7^{25})

= - lo g_{10} (3^{25}) + lo g_{10} (7^{25})

Apply log rule:

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

lo g_{10} (7^{25}) - lo g_{10} (3^{25}) = lo g_{10} (\frac{7 ^{25}}{3 ^{25}})

= lo g_{10} (\frac{7 ^{25}}{3 ^{25}})

Combine same powers :

\frac{x ^{n}}{y ^{n}} = (\frac{x}{y})^{n}

= lo g_{10} ((\frac{7}{3})^{25})

Apply log rule

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

assuming

x \geq 0

= 25 lo g_{10} (\frac{7}{3})

ln (4.4 \cdot 1 0^{9})

10 \cdot lo g_{10} (0.68 \cdot (π \cdot \frac{6.5}{0.0161})^{2})

- \frac{1}{2} lo g_{15} (17) + \frac{1}{2} lo g_{15} (3)

e^{(3^{2} - 1)} 3^{3} + ln (5 \cdot 3^{3}) 3^{2} + 15

\frac{1}{5} ln (\frac{0.267 - 0.017}{0.095 - 0.017})

What is simplify-25log_{10}(3)+25log_{10}(7) ?
The solution to simplify-25log_{10}(3)+25log_{10}(7) is 25log_{10}(7/3)