What is the answer to 10.2^{x^2-4}=320 ?

The answer to 10.2^{x^2-4}=320 is x=sqrt((ln(320))/(ln(10.2))+4),x=-sqrt((ln(320))/(ln(10.2))+4)

Solve for x: 10.2^{x^2-4}=320

The solution is x=sqrt((ln(320))/(ln(10.2))+4),x=-sqrt((ln(320))/(ln(10.2))+4)

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10. 2^{x^{2} - 4} = 320

x = \frac{ln ( 320 )}{ln ( 10.2 )} + 4, x = - \frac{ln ( 320 )}{ln ( 10.2 )} + 4

Decimal Notation

x = 2.54632 \dots, x = - 2.54632 \dots

Solution steps

10. 2^{x^{2} - 4} = 320

Apply exponent rules

(x^{2} - 4) ln (10.2) = ln (320)

Solve

(x^{2} - 4) ln (10.2) = ln (320) : x = \frac{ln ( 320 )}{ln ( 10.2 )} + 4, x = - \frac{ln ( 320 )}{ln ( 10.2 )} + 4

x = \frac{ln ( 320 )}{ln ( 10.2 )} + 4, x = - \frac{ln ( 320 )}{ln ( 10.2 )} + 4

x, e^{2 x} - 5 e^{x} + 4 = 0

2^{x} = 500

ln (e^{3 x}) = 1

2^{x} = 20000

e^{x} x^{2} + 4 e^{x} x + 2 e^{x} = 0

What is the answer to 10.2^{x^2-4}=320 ?
The answer to 10.2^{x^2-4}=320 is x=sqrt((ln(320))/(ln(10.2))+4),x=-sqrt((ln(320))/(ln(10.2))+4)
Solve for x: 10.2^{x^2-4}=320
The solution is x=sqrt((ln(320))/(ln(10.2))+4),x=-sqrt((ln(320))/(ln(10.2))+4)