What is the answer to log_{x}(x+30)=2 ?

The answer to log_{x}(x+30)=2 is x=6

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log_{x}(x+30)=2

lo g_{x} (x + 30) = 2

x = 6

Solution steps

lo g_{x} (x + 30) = 2

Apply log rules

\frac{ln ( x + 30 )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( x + 30 )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (x + 30) = 2 ln (x)

Apply log rules

x + 30 = x^{2}

Solve

x + 30 = x^{2} : x = 6, x = - 5

x = 6, x = - 5

Verify Solutions:

x = 6

True

, x = - 5

False

The solution is

x = 6

lo g_{7} (x) = 1.69

ln (x + 15) - ln (3 - 2 x) = 4 ln (2)

a ln (2) = \frac{a}{4} ln (a)

lo g_{10} (9 x + 1) = 3

lo g_{32} (4) = lo g_{2} (x)