What is the answer to log_{x}(x)+log_{10}(8)=2 ?

The answer to log_{x}(x)+log_{10}(8)=2 is No Solution for x\in\mathbb{R}

Solve for x: log_{x}(x)+log_{10}(8)=2

The solution is No Solution for x\in\mathbb{R}

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lo g_{x} (x) + lo g_{10} (8) = 2

No Solution for x \in R

Solution steps

lo g_{x} (x) + lo g_{10} (8) = 2

Move

lo g_{10} (8)

to the right side

lo g_{x} (x) = 2 - lo g_{10} (8)

Apply log rules

\frac{ln ( x )}{ln ( x )} = 2 - 3 lo g_{10} (2)

Multiply both sides by

ln (x)

\frac{ln ( x )}{ln ( x )} ln (x) = 2 ln (x) - 3 lo g_{10} (2) ln (x)

Simplify

ln (x) = 2 ln (x) - 3 lo g_{10} (2) ln (x)

Subtract

2 ln (x) - 3 lo g_{10} (2) ln (x)

from both sides

ln (x) - (2 ln (x) - 3 lo g_{10} (2) ln (x)) = 2 ln (x) - 3 lo g_{10} (2) ln (x) - (2 ln (x) - 3 lo g_{10} (2) ln (x))

Simplify

- ln (x) + 3 lo g_{10} (2) ln (x) = 0

Factor

- ln (x) + 3 lo g_{10} (2) ln (x) : ln (x) (- 1 + 3 lo g_{10} (2))

ln (x) (- 1 + 3 lo g_{10} (2)) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

ln (x) = 0

Apply log rules

x = 1

Verify Solutions:

x = 1

False

The solution is

No Solution for x \in R

6 + ln (x) = 8

y, x = \frac{ln ( 5 y )}{5}

- 0.688 = lo g_{10} (x)

x, ln (3 x) = 0

lo g_{2} (z + 7) + lo g_{2} (z + 5) = 3

What is the answer to log_{x}(x)+log_{10}(8)=2 ?
The answer to log_{x}(x)+log_{10}(8)=2 is No Solution for x\in\mathbb{R}
Solve for x: log_{x}(x)+log_{10}(8)=2
The solution is No Solution for x\in\mathbb{R}