What is 2.5ln(2x^{-1})-4+0.1x^{1.5} ?

The solution to 2.5ln(2x^{-1})-4+0.1x^{1.5} is 0.1x^{1.5}-ln(x)+2.5ln(2)-1.5

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simplify 2.5ln(2x^{-1})-4+0.1x^{1.5}

simplify

2.5 ln (2 x^{- 1}) - 4 + 0.1 x^{1.5}

0.1 x^{1.5} - ln (x) + 2.5 ln (2) - 1.5

Solution steps

2.5 ln (2 x^{- 1}) - 4 + 0.1 x^{1.5}

Apply log rule:

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

2.5 ln (2 x^{- 1}) = 2.5 ln (2) + 2.5 ln (x^{- 1})

= 2.5 ln (2) + 2.5 ln (x^{- 1}) - 4 + 0.1 x^{1.5}

Apply log rule:

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

ln (x^{- 1}) = - 1 \cdot ln (x)

= 2.5 ln (2) + 2.5 - 1 \cdot ln (x) - 4 + 0.1 x^{1.5}

Multiply:

1 \cdot ln (x) = ln (x)

= 2.5 ln (2) + 2.5 - ln (x) - 4 + 0.1 x^{1.5}

Group like terms

= 0.1 x^{1.5} - ln (x) + 2.5 ln (2) + 2.5 - 4

Add/Subtract the numbers:

2.5 - 4 = - 1.5

= 0.1 x^{1.5} - ln (x) + 2.5 ln (2) - 1.5

ln (x^{2} y^{2} z^{2})

lo g_{10} (13 c d)

ln (x) + ln (x - 2) + ln (4 x)

lo g_{10} (\frac{10 x ^{3}}{y ^{2}})

What is 2.5ln(2x^{-1})-4+0.1x^{1.5} ?
The solution to 2.5ln(2x^{-1})-4+0.1x^{1.5} is 0.1x^{1.5}-ln(x)+2.5ln(2)-1.5