What is the answer to (sqrt(ln(x)))/(ln(sqrt(x)))=3 ?

The answer to (sqrt(ln(x)))/(ln(sqrt(x)))=3 is x=e^{4/9}

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(sqrt(ln(x)))/(ln(sqrt(x)))=3

Solution

\frac{ln ( x )}{ln ( x )} = 3

Solution

x = e^{\frac{4}{9}}

Decimal

x = 1.55962 \dots

Solution steps

\frac{ln ( x )}{ln ( x )} = 3

Multiply both sides by

ln (x)

\frac{ln ( x )}{ln ( x )} ln (x) = 3 ln (x)

Simplify

ln (x) = 3 ln (x)

Apply log rules

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

Rewrite the equation with

ln (x) = u

u = 3 \cdot \frac{1}{2} u

Solve

u = 3 \cdot \frac{1}{2} u : u = \frac{4}{9}, u = 0

u = \frac{4}{9}, u = 0

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = \frac{4}{9} : x = e^{\frac{4}{9}}

Solve

ln (x) = 0 : x = 1

x = e^{\frac{4}{9}}, x = 1

Verify Solutions:

x = e^{\frac{4}{9}}

True

, x = 1

False

The solution is

x = e^{\frac{4}{9}}

Graph

Popular Examples

log_{3}(6x-2)=2

lo g_{3} (6 x - 2) = 2

3ln(5x)=10

3 ln (5 x) = 10

log_{10}(3x)=2

lo g_{10} (3 x) = 2

log_{10}(x)+log_{10}(x-99)=2

lo g_{10} (x) + lo g_{10} (x - 99) = 2

solvefor a,x=ln(a/s)solve for

a, x = ln (\frac{a}{s})

Frequently Asked Questions (FAQ)

What is the answer to (sqrt(ln(x)))/(ln(sqrt(x)))=3 ?
The answer to (sqrt(ln(x)))/(ln(sqrt(x)))=3 is x=e^{4/9}
Solve for x: (sqrt(ln(x)))/(ln(sqrt(x)))=3
The solution is x=e^{4/9}

(sqrt(ln(x)))/(ln(sqrt(x)))=3

Solution

Solution

Graph

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to (sqrt(ln(x)))/(ln(sqrt(x)))=3 ?

Solve for x: (sqrt(ln(x)))/(ln(sqrt(x)))=3