What is ln(1+0.5^4+2*0.5^2)+ln(1+0.5^4-2*0.5^2) ?

The solution to ln(1+0.5^4+2*0.5^2)+ln(1+0.5^4-2*0.5^2) is ln(0.87890625)

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simplify ln(1+0.5^4+20.5^2)+ln(1+0.5^4-20.5^2)

simplify

ln (1 + 0. 5^{4} + 2 \cdot 0. 5^{2}) + ln (1 + 0. 5^{4} - 2 \cdot 0. 5^{2})

ln (0.87890625)

Decimal Notation

- 0.12907 \dots

Solution steps

ln (1 + 0. 5^{4} + 2 \cdot 0. 5^{2}) + ln (1 + 0. 5^{4} - 2 \cdot 0. 5^{2})

Apply log rule:

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

ln (1 + 0. 5^{4} + 2 \cdot 0. 5^{2}) + ln (1 + 0. 5^{4} - 2 \cdot 0. 5^{2}) = ln ((1 + 2 \cdot 0. 5^{2} + 0. 5^{4}) (1 + 0. 5^{4} - 2 \cdot 0. 5^{2}))

= ln ((1 + 2 \cdot 0. 5^{2} + 0. 5^{4}) (1 + 0. 5^{4} - 2 \cdot 0. 5^{2}))

(1 + 0. 5^{4} + 2 \cdot 0. 5^{2}) (1 + 0. 5^{4} - 2 \cdot 0. 5^{2}) = 0.87890625

= ln (0.87890625)

\frac{8}{5} ln (a) + \frac{9}{10} ln (b)

3 lo g_{6} (y - 3) - 4 lo g_{6} (y + 2)

lo g_{10} (2) \cdot \frac{1}{2}

ln (\frac{39}{40})

6 + 2 ln (6) - 2 ln (\frac{20}{3})

What is ln(1+0.5^4+2*0.5^2)+ln(1+0.5^4-2*0.5^2) ?
The solution to ln(1+0.5^4+2*0.5^2)+ln(1+0.5^4-2*0.5^2) is ln(0.87890625)