What is the answer to log_{a}(49)= 2/3 ?

The answer to log_{a}(49)= 2/3 is a=343

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log_{a}(49)= 2/3

lo g_{a} (49) = \frac{2}{3}

a = 343

Solution steps

lo g_{a} (49) = \frac{2}{3}

Apply log rules

\frac{1}{lo g _{49} ( a )} = \frac{2}{3}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

1 \cdot 3 = lo g_{49} (a) \cdot 2

Simplify

3 = lo g_{49} (a) \cdot 2

Switch sides

lo g_{49} (a) \cdot 2 = 3

Divide both sides by

2

lo g_{49} (a) = \frac{3}{2}

Apply log rules

a = 343

Verify Solutions:

a = 343

True

The solution is

a = 343

lo g_{x - 3} (2 x^{2} - 11 x + 16) = 2

lo g_{10} (x) (343) = 3

x, 0.22 = ln (x)

lo g_{10} (x^{4}) = \frac{1}{4}

6 ln (x) = 7.2

What is the answer to log_{a}(49)= 2/3 ?
The answer to log_{a}(49)= 2/3 is a=343
Solve for a: log_{a}(49)= 2/3
The solution is a=343