What is the answer to log_{x}(25)=log_{5}(x) ?

The answer to log_{x}(25)=log_{5}(x) is x=5^{sqrt(2)},x= 1/(5^{sqrt(2))}

Solve for x: log_{x}(25)=log_{5}(x)

The solution is x=5^{sqrt(2)},x= 1/(5^{sqrt(2))}

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lo g_{x} (25) = lo g_{5} (x)

x = 5^{2}, x = \frac{1}{5 ^{2}}

Decimal Notation

x = 9.73851 \dots, x = 0.10268 \dots

Solution steps

lo g_{x} (25) = lo g_{5} (x)

Apply log rules

\frac{2}{lo g _{5} ( x )} = lo g_{5} (x)

Rewrite the equation with

lo g_{5} (x) = u

\frac{2}{u} = u

Solve

\frac{2}{u} = u : u = 2, u = - 2

u = 2, u = - 2

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

lo g_{5} (x) = 2 : x = 5^{2}

Solve

lo g_{5} (x) = - 2 : x = \frac{1}{5 ^{2}}

x = 5^{2}, x = \frac{1}{5 ^{2}}

Verify Solutions:

x = 5^{2}

True

, x = \frac{1}{5 ^{2}}

True

The solutions are

x = 5^{2}, x = \frac{1}{5 ^{2}}

lo g_{2} (a) + lo g_{a} (4) = 3

lo g_{3} (x - 1) = 1 + lo g_{3} (3 x + 2)

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

ln (x^{7}) - ln (x^{2}) = 5

lo g_{8} (x) = - 1

What is the answer to log_{x}(25)=log_{5}(x) ?
The answer to log_{x}(25)=log_{5}(x) is x=5^{sqrt(2)},x= 1/(5^{sqrt(2))}
Solve for x: log_{x}(25)=log_{5}(x)
The solution is x=5^{sqrt(2)},x= 1/(5^{sqrt(2))}