What is 1+8ln(16(2)^2) ?

The solution to 1+8ln(16(2)^2) is 1+48ln(2)

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simplify 1+8ln(16(2)^2)

simplify

1 + 8 ln (16 (2)^{2})

1 + 48 ln (2)

Decimal Notation

34.27106 \dots

Solution steps

1 + 8 ln (16 (2)^{2})

Apply log rule:

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

8 ln (16 \cdot 2^{2}) = 8 ln (16) + 8 ln (2^{2})

= 1 + 8 ln (16) + 8 ln (2^{2})

Apply log rule:

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

ln (2^{2}) = 2 ln (2)

= 1 + 8 ln (16) + 8 \cdot 2 ln (2)

Multiply the numbers:

8 \cdot 2 = 16

= 1 + 8 ln (16) + 16 ln (2)

8 ln (16) = 32 ln (2)

= 1 + 32 ln (2) + 16 ln (2)

Add similar elements:

32 ln (2) + 16 ln (2) = 48 ln (2)

= 1 + 48 ln (2)

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