What is the answer to log_{x+3}(9)=log_{5}(3) ?

The answer to log_{x+3}(9)=log_{5}(3) is x=9^{1/(log_{5)(3)}}-3

Solve for x: log_{x+3}(9)=log_{5}(3)

The solution is x=9^{1/(log_{5)(3)}}-3

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lo g_{x + 3} (9) = lo g_{5} (3)

x = 9^{\frac{1}{l o g _{5} ( 3 )}} - 3

Decimal Notation

x = 22

Solution steps

lo g_{x + 3} (9) = lo g_{5} (3)

Apply log rules

\frac{1}{lo g _{9} ( x + 3 )} = lo g_{5} (3)

Multiply both sides by

lo g_{9} (x + 3)

\frac{1}{lo g _{9} ( x + 3 )} lo g_{9} (x + 3) = lo g_{5} (3) lo g_{9} (x + 3)

Simplify

1 = lo g_{5} (3) lo g_{9} (x + 3)

Switch sides

lo g_{5} (3) lo g_{9} (x + 3) = 1

Divide both sides by

lo g_{5} (3)

lo g_{9} (x + 3) = \frac{1}{lo g _{5} ( 3 )}

Apply log rules

x + 3 = 9^{\frac{1}{l o g _{5} ( 3 )}}

Solve

x + 3 = 9^{\frac{1}{l o g _{5} ( 3 )}} : x = 9^{\frac{1}{l o g _{5} ( 3 )}} - 3

x = 9^{\frac{1}{l o g _{5} ( 3 )}} - 3

Verify Solutions:

x = 9^{\frac{1}{l o g _{5} ( 3 )}} - 3

True

The solution is

x = 9^{\frac{1}{l o g _{5} ( 3 )}} - 3

lo g_{a} (49) = 2

3 ln (x + 3) = 6

1 = \frac{1}{n} lo g_{10} (n)

x, y = ln (x + y - 5)

lo g_{10} (x) = - 6.2

What is the answer to log_{x+3}(9)=log_{5}(3) ?
The answer to log_{x+3}(9)=log_{5}(3) is x=9^{1/(log_{5)(3)}}-3
Solve for x: log_{x+3}(9)=log_{5}(3)
The solution is x=9^{1/(log_{5)(3)}}-3