What is the answer to log_{x}(49)=4 ?

The answer to log_{x}(49)=4 is x=sqrt(7)

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log_{x}(49)=4

lo g_{x} (49) = 4

x = 7

Decimal Notation

x = 2.64575 \dots

Solution steps

lo g_{x} (49) = 4

Apply log rules

\frac{1}{lo g _{49} ( x )} = 4

Multiply both sides by

lo g_{49} (x)

\frac{1}{lo g _{49} ( x )} lo g_{49} (x) = 4 lo g_{49} (x)

Simplify

1 = 4 lo g_{49} (x)

Switch sides

4 lo g_{49} (x) = 1

Divide both sides by

4

lo g_{49} (x) = \frac{1}{4}

Apply log rules

x = 7

Verify Solutions:

x = 7

True

The solution is

x = 7

lo g_{10} (\frac{1}{2 x + 3}) = - 2

lo g_{6} (x + 3) + lo g_{6} (x - 2) = 1

0.43 = lo g_{10} (x)

ln (x + 5) + ln (3 x - 1) = 6 ln (2)

lo g_{0.2} (x) = - 3