What is the answer to ln((x-3)^4)=8 ?

The answer to ln((x-3)^4)=8 is x=e^2+3,x=-e^2+3

Solve for x: ln((x-3)^4)=8

The solution is x=e^2+3,x=-e^2+3

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ln ((x - 3)^{4}) = 8

x = e^{2} + 3, x = - e^{2} + 3

Decimal Notation

x = 10.38905 \dots, x = - 4.38905 \dots

Solution steps

ln ((x - 3)^{4}) = 8

Apply exponent rule:

a^{2 \cdot n} = (a^{2})^{n}

(x - 3)^{4} = ((x - 3)^{2})^{2}

ln (((x - 3)^{2})^{2}) = 8

Apply log rules

(x - 3)^{2} = e^{4}

Solve

(x - 3)^{2} = e^{4} : x = e^{2} + 3, x = - e^{2} + 3

x = e^{2} + 3, x = - e^{2} + 3

Verify Solutions:

x = e^{2} + 3

True

, x = - e^{2} + 3

True

The solutions are

x = e^{2} + 3, x = - e^{2} + 3

lo g_{2} (x + 4) + lo g_{2} (x - 2) = 4

ln (7 x + e) = 7

lo g_{x} (x^{2} - 2 x - 1) = 2

ln (x) = 1.2

ln (x) = 1.3

What is the answer to ln((x-3)^4)=8 ?
The answer to ln((x-3)^4)=8 is x=e^2+3,x=-e^2+3
Solve for x: ln((x-3)^4)=8
The solution is x=e^2+3,x=-e^2+3