What is the answer to ln(16^x)=25 ?

The answer to ln(16^x)=25 is x=(25)/(4ln(2))

Solve for x: ln(16^x)=25

The solution is x=(25)/(4ln(2))

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ln (1 6^{x}) = 25

x = \frac{25}{4 ln ( 2 )}

Decimal Notation

x = 9.01684 \dots

Solution steps

ln (1 6^{x}) = 25

Rewrite the equation with

1 6^{x} = u

ln (u) = 25

Solve

ln (u) = 25 : u = e^{25}

u = e^{25}

Substitute back

u = 1 6^{x},

solve for

x

Solve

1 6^{x} = e^{25} : x = \frac{25}{4 ln ( 2 )}

x = \frac{25}{4 ln ( 2 )}

(3^{x})^{2} - 2 \cdot 3^{x} - 3 = 0

(\frac{1}{9})^{x} = 729

1 6^{- 7 x} = 72

5^{2 x - 1} = 6

5^{2 x + 4} = \frac{1}{625}

What is the answer to ln(16^x)=25 ?
The answer to ln(16^x)=25 is x=(25)/(4ln(2))
Solve for x: ln(16^x)=25
The solution is x=(25)/(4ln(2))