What is the answer to log_{x}(16/9)=2 ?

The answer to log_{x}(16/9)=2 is x=e^{(ln(16/9))/2}

Solve for x: log_{x}(16/9)=2

The solution is x=e^{(ln(16/9))/2}

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lo g_{x} (\frac{16}{9}) = 2

x = e^{\frac{l n ( \frac{16}{9} )}{2}}

Decimal Notation

x = 1.33333 \dots

Solution steps

lo g_{x} (\frac{16}{9}) = 2

Apply log rules

\frac{ln ( \frac{16}{9} )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( \frac{16}{9} )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (\frac{16}{9}) = 2 ln (x)

Switch sides

2 ln (x) = ln (\frac{16}{9})

Divide both sides by

2

ln (x) = \frac{ln ( \frac{16}{9} )}{2}

Apply log rules

x = e^{\frac{l n ( \frac{16}{9} )}{2}}

Verify Solutions:

x = e^{\frac{l n ( \frac{16}{9} )}{2}}

True

The solution is

x = e^{\frac{l n ( \frac{16}{9} )}{2}}

lo g_{27} (8 1^{x}) = x - 1

ln (x + 3) - ln (4 - 3 x) = 2 ln (2)

lo g_{10} (x) + lo g_{10} (x + 5) = 9

ln (x) = 3 ln (x)

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

What is the answer to log_{x}(16/9)=2 ?
The answer to log_{x}(16/9)=2 is x=e^{(ln(16/9))/2}
Solve for x: log_{x}(16/9)=2
The solution is x=e^{(ln(16/9))/2}