What is the answer to log_{sqrt(5)}(25^{4x-1})=3 ?

The answer to log_{sqrt(5)}(25^{4x-1})=3 is x= 7/16

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log_{sqrt(5)}(25^{4x-1})=3

lo g_{5} (2 5^{4 x - 1}) = 3

x = \frac{7}{16}

Decimal Notation

x = 0.4375

Solution steps

lo g_{5} (2 5^{4 x - 1}) = 3

Rewrite the equation with

2 5^{4 x - 1} = u

lo g_{5} (u) = 3

Solve

lo g_{5} (u) = 3 : u = 55

u = 55

Substitute back

u = 2 5^{4 x - 1},

solve for

x

Solve

2 5^{4 x - 1} = 55 : x = \frac{7}{16}

x = \frac{7}{16}

(\frac{1}{27})^{x} = \frac{1}{3}

2 (2^{2 x}) - 5 (2^{x}) + 2 = 0

2^{x + 1} + 2^{x} = 48

4 e^{3 x} = 9

What is the answer to log_{sqrt(5)}(25^{4x-1})=3 ?
The answer to log_{sqrt(5)}(25^{4x-1})=3 is x= 7/16
Solve for x: log_{sqrt(5)}(25^{4x-1})=3
The solution is x= 7/16