What is 5ln|10^x(2x^6+2)^2|+9ln|7x^2-8| ?

The solution to 5ln|10^x(2x^6+2)^2|+9ln|7x^2-8| is ln(100000^x|7x^2-8|^9(2x^6+2)^{10})

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simplify 5ln|10^x(2x^6+2)^2|+9ln|7x^2-8|

simplify

5 ln 1 0^{x} (2 x^{6} + 2)^{2} + 9 ln 7 x^{2} - 8

ln (10000 0^{x} 7 x^{2} - 8^{9} (2 x^{6} + 2)^{10})

Solution steps

5 ln 1 0^{x} (2 x^{6} + 2)^{2} + 9 ln 7 x^{2} - 8

Apply log rule:

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

5 ln 1 0^{x} (2 x^{6} + 2)^{2} = ln (1 0^{x} (2 x^{6} + 2)^{2}^{5})

= ln (1 0^{x} (2 x^{6} + 2)^{2}^{5}) + 9 ln 7 x^{2} - 8

Apply log rule:

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

9 ln 7 x^{2} - 8 = ln (7 x^{2} - 8^{9})

= ln (1 0^{x} (2 x^{6} + 2)^{2}^{5}) + ln (7 x^{2} - 8^{9})

Apply log rule:

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

ln (1 0^{x} (2 x^{6} + 2)^{2}^{5}) + ln (7 x^{2} - 8^{9}) = ln (7 x^{2} - 8^{9} 1 0^{x} (2 x^{6} + 2)^{2}^{5})

= ln (7 x^{2} - 8^{9} 1 0^{x} (2 x^{6} + 2)^{2}^{5})

Simplify

1 0^{x} (2 x^{6} + 2)^{2}^{5} 7 x^{2} - 8^{9} : 10000 0^{x} 7 x^{2} - 8^{9} (2 x^{6} + 2)^{10}

= ln (10000 0^{x} 7 x^{2} - 8^{9} (2 x^{6} + 2)^{10})

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What is 5ln|10^x(2x^6+2)^2|+9ln|7x^2-8| ?
The solution to 5ln|10^x(2x^6+2)^2|+9ln|7x^2-8| is ln(100000^x|7x^2-8|^9(2x^6+2)^{10})