What is the answer to log_{2}(5^{2x}+3)=5 ?

The answer to log_{2}(5^{2x}+3)=5 is x=(ln(29))/(2ln(5))

Solve for x: log_{2}(5^{2x}+3)=5

The solution is x=(ln(29))/(2ln(5))

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lo g_{2} (5^{2 x} + 3) = 5

x = \frac{ln ( 29 )}{2 ln ( 5 )}

Decimal Notation

x = 1.04610 \dots

Solution steps

lo g_{2} (5^{2 x} + 3) = 5

Rewrite the equation with

5^{2 x} = u

lo g_{2} (u + 3) = 5

Solve

lo g_{2} (u + 3) = 5 : u = 29

u = 29

Substitute back

u = 5^{2 x},

solve for

x

Solve

5^{2 x} = 29 : x = \frac{ln ( 29 )}{2 ln ( 5 )}

x = \frac{ln ( 29 )}{2 ln ( 5 )}

5 e^{x} - 2 e^{2 x} = 0

y, x y - e^{x} + e^{y} = 0

(\frac{1}{27})^{x} = 9

y, x = 4^{y}

t^{n} e^{a t}

What is the answer to log_{2}(5^{2x}+3)=5 ?
The answer to log_{2}(5^{2x}+3)=5 is x=(ln(29))/(2ln(5))
Solve for x: log_{2}(5^{2x}+3)=5
The solution is x=(ln(29))/(2ln(5))