What is the answer to log_{a}(2048)=11 ?

The answer to log_{a}(2048)=11 is a=2

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log_{a}(2048)=11

lo g_{a} (2048) = 11

a = 2

Solution steps

lo g_{a} (2048) = 11

Apply log rules

\frac{1}{lo g _{2048} ( a )} = 11

Multiply both sides by

lo g_{2048} (a)

\frac{1}{lo g _{2048} ( a )} lo g_{2048} (a) = 11 lo g_{2048} (a)

Simplify

1 = 11 lo g_{2048} (a)

Switch sides

11 lo g_{2048} (a) = 1

Divide both sides by

11

lo g_{2048} (a) = \frac{1}{11}

Apply log rules

a = 2

Verify Solutions:

a = 2

True

The solution is

a = 2

ln (3) + ln (2 x + 5) = 2 ln (x + 2)

lo g_{20} (x) = 1 + lo g_{20} (10)

2 lo g_{10} (x + 5) - lo g_{3} (9) = 2

ln (5 x + 4) = 3

ln (5 x + 4) = 0