What is the answer to ln((x-2)^4)=7 ?

The answer to ln((x-2)^4)=7 is x=sqrt(e^{7/2)}+2,x=-sqrt(e^{7/2)}+2

Solve for x: ln((x-2)^4)=7

The solution is x=sqrt(e^{7/2)}+2,x=-sqrt(e^{7/2)}+2

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ln ((x - 2)^{4}) = 7

x = e^{\frac{7}{2}} + 2, x = - e^{\frac{7}{2}} + 2

Decimal Notation

x = 7.75460 \dots, x = - 3.75460 \dots

Solution steps

ln ((x - 2)^{4}) = 7

Apply exponent rule:

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

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

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

Apply log rules

(x - 2)^{2} = e^{\frac{7}{2}}

Solve

(x - 2)^{2} = e^{\frac{7}{2}} : x = e^{\frac{7}{2}} + 2, x = - e^{\frac{7}{2}} + 2

x = e^{\frac{7}{2}} + 2, x = - e^{\frac{7}{2}} + 2

Verify Solutions:

x = e^{\frac{7}{2}} + 2

True

, x = - e^{\frac{7}{2}} + 2

True

The solutions are

x = e^{\frac{7}{2}} + 2, x = - e^{\frac{7}{2}} + 2

2 ln (7 x) = - 4

lo g_{2} (4 x) + lo g_{2} (x - 2) = 5

x, 4 = 2 lo g_{9} (6 x + 6)

\frac{ln ( 2 )}{ln ( a )} = 11

17 - ln (3 - x) = 0

What is the answer to ln((x-2)^4)=7 ?
The answer to ln((x-2)^4)=7 is x=sqrt(e^{7/2)}+2,x=-sqrt(e^{7/2)}+2
Solve for x: ln((x-2)^4)=7
The solution is x=sqrt(e^{7/2)}+2,x=-sqrt(e^{7/2)}+2