What is the answer to log_{b}(3^b)= b/2 ?

The answer to log_{b}(3^b)= b/2 is b=9

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log_{b}(3^b)= b/2

lo g_{b} (3^{b}) = \frac{b}{2}

b = 9

Solution steps

lo g_{b} (3^{b}) = \frac{b}{2}

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

b^{l o g_{b} (3^{b})} = b^{\frac{b}{2}}

Simplify

b^{l o g_{b} (3^{b})} : 3^{b}

3^{b} = b^{\frac{b}{2}}

Solve

3^{b} = b^{\frac{b}{2}} : b = 9

b = 9

Verify Solutions:

b = 9

True

The solution is

b = 9

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

lo g_{10} (2 x + 1) = 2

- 7 lo g_{5} (4 x) = - 14

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

lo g_{16} (x) = \frac{1}{4}

What is the answer to log_{b}(3^b)= b/2 ?
The answer to log_{b}(3^b)= b/2 is b=9
Solve for b: log_{b}(3^b)= b/2
The solution is b=9