What is the answer to log_{x}(10)=log_{10}(x) ?

The answer to log_{x}(10)=log_{10}(x) is x=10,x= 1/10

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log_{x}(10)=log_{10}(x)

lo g_{x} (10) = lo g_{10} (x)

x = 10, x = \frac{1}{10}

Decimal Notation

x = 10, x = 0.1

Solution steps

lo g_{x} (10) = lo g_{10} (x)

Apply log rules

\frac{1}{lo g _{10} ( x )} = lo g_{10} (x)

Rewrite the equation with

lo g_{10} (x) = u

\frac{1}{u} = u

Solve

\frac{1}{u} = u : u = 1, u = - 1

u = 1, u = - 1

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

lo g_{10} (x) = 1 : x = 10

Solve

lo g_{10} (x) = - 1 : x = \frac{1}{10}

x = 10, x = \frac{1}{10}

Verify Solutions:

x = 10

True

, x = \frac{1}{10}

True

The solutions are

x = 10, x = \frac{1}{10}

lo g_{4} (- 8 - 4 x) = 1

ln (5 x) = 3

1 + 2 lo g_{3} (x) = lo g_{3} (28 x - 9)

ln (10 - 3 x) = ln (- 4 x)

5 + ln (x + 3) = 2

What is the answer to log_{x}(10)=log_{10}(x) ?
The answer to log_{x}(10)=log_{10}(x) is x=10,x= 1/10
Solve for x: log_{x}(10)=log_{10}(x)
The solution is x=10,x= 1/10