What is the answer to log_{x}(5)+log_{x}(12)=7 ?

The answer to log_{x}(5)+log_{x}(12)=7 is x=e^{(ln(60))/7}

Solve for x: log_{x}(5)+log_{x}(12)=7

The solution is x=e^{(ln(60))/7}

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lo g_{x} (5) + lo g_{x} (12) = 7

x = e^{\frac{l n ( 60 )}{7}}

Decimal Notation

x = 1.79482 \dots

Solution steps

lo g_{x} (5) + lo g_{x} (12) = 7

Apply log rules

\frac{ln ( 5 \cdot 12 )}{ln ( x )} = 7

Multiply both sides by

ln (x)

\frac{ln ( 5 \cdot 12 )}{ln ( x )} ln (x) = 7 ln (x)

Simplify

ln (60) = 7 ln (x)

Switch sides

7 ln (x) = ln (60)

Divide both sides by

7

ln (x) = \frac{ln ( 60 )}{7}

Apply log rules

x = e^{\frac{l n ( 60 )}{7}}

Verify Solutions:

x = e^{\frac{l n ( 60 )}{7}}

True

The solution is

x = e^{\frac{l n ( 60 )}{7}}

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

lo g_{10} (x) + lo g_{10} (x - 7) = 2

lo g_{2} (x) + lo g_{4} (x) = 3

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

lo g_{2} (x + 4) = 2 - lo g_{2} (x + 7)

What is the answer to log_{x}(5)+log_{x}(12)=7 ?
The answer to log_{x}(5)+log_{x}(12)=7 is x=e^{(ln(60))/7}
Solve for x: log_{x}(5)+log_{x}(12)=7
The solution is x=e^{(ln(60))/7}