What is the answer to log_{y}(100)=log_{10}(y) ?

The answer to log_{y}(100)=log_{10}(y) is y=10^{sqrt(2)},y= 1/(10^{sqrt(2))}

Solve for y: log_{y}(100)=log_{10}(y)

The solution is y=10^{sqrt(2)},y= 1/(10^{sqrt(2))}

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lo g_{y} (100) = lo g_{10} (y)

y = 1 0^{2}, y = \frac{1}{1 0 ^{2}}

Decimal Notation

y = 25.95455 \dots, y = 0.03852 \dots

Solution steps

lo g_{y} (100) = lo g_{10} (y)

Apply log rules

\frac{2}{lo g _{10} ( y )} = lo g_{10} (y)

Rewrite the equation with

lo g_{10} (y) = u

\frac{2}{u} = u

Solve

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

u = 2, u = - 2

Substitute back

u = lo g_{10} (y),

solve for

y

Solve

lo g_{10} (y) = 2 : y = 1 0^{2}

Solve

lo g_{10} (y) = - 2 : y = \frac{1}{1 0 ^{2}}

y = 1 0^{2}, y = \frac{1}{1 0 ^{2}}

Verify Solutions:

y = 1 0^{2}

True

, y = \frac{1}{1 0 ^{2}}

True

The solutions are

y = 1 0^{2}, y = \frac{1}{1 0 ^{2}}

\frac{ln ( x + 3 )}{ln ( x + 1 )} = 2

ln (2) + ln (x) = 5

5 lo g_{4} (64 k) = 18

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

lo g_{e} (2 x) = 1

What is the answer to log_{y}(100)=log_{10}(y) ?
The answer to log_{y}(100)=log_{10}(y) is y=10^{sqrt(2)},y= 1/(10^{sqrt(2))}
Solve for y: log_{y}(100)=log_{10}(y)
The solution is y=10^{sqrt(2)},y= 1/(10^{sqrt(2))}