What is 0.026ln(0.095)+0.416ln(10) ?

The solution to 0.026ln(0.095)+0.416ln(10) is ln(2.45143…)

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simplify 0.026ln(0.095)+0.416ln(10)

simplify

0.026 ln (0.095) + 0.416 ln (10)

ln (2.45143 \dots)

Decimal Notation

0.89667 \dots

Solution steps

0.026 ln (0.095) + 0.416 ln (10)

Apply log rule:

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

0.026 ln (0.095) = ln (0.09 5^{0.026})

= ln (0.09 5^{0.026}) + 0.416 ln (10)

Apply log rule:

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

0.416 ln (10) = ln (1 0^{0.416})

= ln (0.09 5^{0.026}) + ln (1 0^{0.416})

Apply log rule:

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

ln (0.09 5^{0.026}) + ln (1 0^{0.416}) = ln (1 0^{0.416} \cdot 0.09 5^{0.026})

= ln (1 0^{0.416} \cdot 0.09 5^{0.026})

0.09 5^{0.026} \cdot 1 0^{0.416} = 2.45143 \dots

= ln (2.45143 \dots)

- ln (\frac{1}{2})

lo g_{2} (3) + 4 lo g_{2} (x) - 2 lo g_{2} (y)

lo g_{10} (a) + 2 lo g_{10} (b) - 3 lo g_{10} (c)

ln ((\frac{1}{x})^{\frac{1}{l n ( x )}})

ln (\frac{486}{271})

What is 0.026ln(0.095)+0.416ln(10) ?
The solution to 0.026ln(0.095)+0.416ln(10) is ln(2.45143…)