What is 99+70log_{10}(1.5)+50log_{10}(0.37) ?

The solution to 99+70log_{10}(1.5)+50log_{10}(0.37) is 99+log_{10}(5.45098E-10)

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simplify 99+70log_{10}(1.5)+50log_{10}(0.37)

simplify

99 + 70 lo g_{10} (1.5) + 50 lo g_{10} (0.37)

99 + lo g_{10} (5.45098 E - 10)

Decimal Notation

89.73647 \dots

Solution steps

99 + 70 lo g_{10} (1.5) + 50 lo g_{10} (0.37)

Apply log rule:

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

70 lo g_{10} (1.5) = lo g_{10} (1. 5^{70})

= 99 + lo g_{10} (1. 5^{70}) + 50 lo g_{10} (0.37)

Apply log rule:

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

50 lo g_{10} (0.37) = lo g_{10} (0.3 7^{50})

= 99 + lo g_{10} (1. 5^{70}) + lo g_{10} (0.3 7^{50})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} (1. 5^{70}) + lo g_{10} (0.3 7^{50}) = lo g_{10} (0.3 7^{50} \cdot 1. 5^{70})

= 99 + lo g_{10} (0.3 7^{50} \cdot 1. 5^{70})

1. 5^{70} \cdot 0.3 7^{50} = 5.45098 E - 10

= 99 + lo g_{10} (5.45098 E - 10)

\frac{3 ln ( 6 ) - 4 ln ( 15 )}{- 2 ln ( 15 ) - ln ( 6 )}

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9 lo g_{8} (x) + 18 lo g_{8} (y)

lo g_{10} (\frac{x ( x + 4 )}{( x + 6 ) ^{9}})

lo g_{10} (x) - 4 lo g_{10} (y) + 2 lo g_{10} (z)

What is 99+70log_{10}(1.5)+50log_{10}(0.37) ?
The solution to 99+70log_{10}(1.5)+50log_{10}(0.37) is 99+log_{10}(5.45098E-10)