What is the answer to log_{x}(25)+log_{x}(5)= 1/2 ?

The answer to log_{x}(25)+log_{x}(5)= 1/2 is x=15625

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log_{x}(25)+log_{x}(5)= 1/2

lo g_{x} (25) + lo g_{x} (5) = \frac{1}{2}

x = 15625

Solution steps

lo g_{x} (25) + lo g_{x} (5) = \frac{1}{2}

Apply log rules

\frac{ln ( 25 \cdot 5 )}{ln ( x )} = \frac{1}{2}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

ln (25 \cdot 5) \cdot 2 = ln (x) \cdot 1

Apply log rules

15625 = x

Switch sides

x = 15625

Verify Solutions:

x = 15625

True

The solution is

x = 15625

lo g_{10} (x) + lo g_{10} (x^{4}) = 5

lo g_{2} (x^{2} + 7 x) = 3

2 \cdot lo g_{2} (y) + 3 \cdot lo g_{y} (2) = 7

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

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

What is the answer to log_{x}(25)+log_{x}(5)= 1/2 ?
The answer to log_{x}(25)+log_{x}(5)= 1/2 is x=15625
Solve for x: log_{x}(25)+log_{x}(5)= 1/2
The solution is x=15625