What is the answer to 4^{x^2}-4= 25/9 ?

The answer to 4^{x^2}-4= 25/9 is x=sqrt((ln(61/9))/(2ln(2))),x=-sqrt((ln(61/9))/(2ln(2)))

Solve for x: 4^{x^2}-4= 25/9

The solution is x=sqrt((ln(61/9))/(2ln(2))),x=-sqrt((ln(61/9))/(2ln(2)))

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4^{x^{2}} - 4 = \frac{25}{9}

x = \frac{ln ( \frac{61}{9} )}{2 ln ( 2 )}, x = - \frac{ln ( \frac{61}{9} )}{2 ln ( 2 )}

Decimal Notation

x = 1.17490 \dots, x = - 1.17490 \dots

Solution steps

4^{x^{2}} - 4 = \frac{25}{9}

Move

4

to the right side

4^{x^{2}} = \frac{61}{9}

Apply exponent rules

x^{2} ln (4) = ln (\frac{61}{9})

Solve

x^{2} ln (4) = ln (\frac{61}{9}) : x = \frac{ln ( \frac{61}{9} )}{2 ln ( 2 )}, x = - \frac{ln ( \frac{61}{9} )}{2 ln ( 2 )}

x = \frac{ln ( \frac{61}{9} )}{2 ln ( 2 )}, x = - \frac{ln ( \frac{61}{9} )}{2 ln ( 2 )}

2^{13 x} = 8

3^{2 x} = 2 7^{x + 1}

e^{x + 2} = e

e^{x} = e - 1

(\frac{1}{3})^{x - 3} = 9

What is the answer to 4^{x^2}-4= 25/9 ?
The answer to 4^{x^2}-4= 25/9 is x=sqrt((ln(61/9))/(2ln(2))),x=-sqrt((ln(61/9))/(2ln(2)))
Solve for x: 4^{x^2}-4= 25/9
The solution is x=sqrt((ln(61/9))/(2ln(2))),x=-sqrt((ln(61/9))/(2ln(2)))