What is simplify-0.7log_{10}(20.7)-0.3log_{10}(20.3) ?

The solution to simplify-0.7log_{10}(20.7)-0.3log_{10}(20.3) is -0.7log_{10}(207)-0.3log_{10}(203)+1

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simplify-0.7log_{10}(20.7)-0.3log_{10}(20.3)

simplify

- 0.7 lo g_{10} (20.7) - 0.3 lo g_{10} (20.3)

- 0.7 lo g_{10} (207) - 0.3 lo g_{10} (203) + 1

Decimal

- 1.31342 \dots

Solution steps

- 0.7 lo g_{10} (20.7) - 0.3 lo g_{10} (20.3)

- 0.7 lo g_{10} (20.7) = - 0.7 lo g_{10} (\frac{207}{10})

20.3 = \frac{203}{10}

= - 0.7 lo g_{10} (\frac{207}{10}) - 0.3 lo g_{10} (\frac{203}{10})

- 0.7 lo g_{10} (\frac{207}{10}) = - lo g_{10} ((\frac{207}{10})^{0.7})

- 0.3 lo g_{10} (\frac{203}{10}) = - lo g_{10} ((\frac{203}{10})^{0.3})

= - lo g_{10} ((\frac{207}{10})^{0.7}) - lo g_{10} ((\frac{203}{10})^{0.3})

Apply log rule:

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

- lo g_{10} ((\frac{203}{10})^{0.3}) - lo g_{10} ((\frac{207}{10})^{0.7}) = lo g_{10} ((\frac{203}{10})^{0.3} (\frac{207}{10})^{0.7})

= - lo g_{10} ((\frac{203}{10})^{0.3} (\frac{207}{10})^{0.7})

Simplify

(\frac{203}{10})^{0.3} (\frac{207}{10})^{0.7} : \frac{20 3 ^{0.3} \cdot 20 7 ^{0.7}}{10}

= - lo g_{10} (\frac{20 3 ^{0.3} \cdot 20 7 ^{0.7}}{10})

Simplify

lo g_{10} (\frac{20 3 ^{0.3} \cdot 20 7 ^{0.7}}{10}) : 0.3 lo g_{10} (203) + lo g_{10} (20 7^{0.7}) - 1

= - (0.3 lo g_{10} (203) + lo g_{10} (20 7^{0.7}) - 1)

lo g_{10} (20 7^{0.7}) + 0.3 lo g_{10} (203) - 1 = lo g_{10} (20 7^{0.7} \cdot 20 3^{0.3}) - 1

= - (lo g_{10} (20 7^{0.7} \cdot 20 3^{0.3}) - 1)

Distribute parentheses

= - (lo g_{10} (20 7^{0.7} \cdot 20 3^{0.3})) - (- 1)

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - lo g_{10} (20 7^{0.7} \cdot 20 3^{0.3}) + 1

lo g_{10} (20 7^{0.7} \cdot 20 3^{0.3}) = 0.7 lo g_{10} (207) + 0.3 lo g_{10} (203)

= - (0.7 lo g_{10} (207) + 0.3 lo g_{10} (203)) + 1

Apply the distributive law:

- (a + b) = - a - b

- (0.7 lo g_{10} (207) + 0.3 lo g_{10} (203)) = - 0.7 lo g_{10} (207) - 0.3 lo g_{10} (203)

= - 0.7 lo g_{10} (207) - 0.3 lo g_{10} (203) + 1

6 lo g_{10} (x) - lo g_{10} (17)

\frac{1}{0.02} ln (35 (e^{0.01} - e^{- 0.02}))

ln (\frac{( 1 - 1.25 )}{0.075}) - 1

\frac{1}{4} ln ∣ x ∣ - \frac{1}{8} ln x^{2} + 4 + C

3 ln (3) + 6 ln (2)

What is simplify-0.7log_{10}(20.7)-0.3log_{10}(20.3) ?
The solution to simplify-0.7log_{10}(20.7)-0.3log_{10}(20.3) is -0.7log_{10}(207)-0.3log_{10}(203)+1