What is the answer to log_{36}(6^a)=a+1 ?

The answer to log_{36}(6^a)=a+1 is a=-2

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log_{36}(6^a)=a+1

lo g_{36} (6^{a}) = a + 1

a = - 2

Solution steps

lo g_{36} (6^{a}) = a + 1

f (x) = g (x),

then

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

3 6^{l o g_{36} (6^{a})} = 3 6^{a + 1}

Simplify

3 6^{l o g_{36} (6^{a})} : 6^{a}

6^{a} = 3 6^{a + 1}

Solve

6^{a} = 3 6^{a + 1} : a = - 2

a = - 2

Verify Solutions:

a = - 2

True

The solution is

a = - 2

ln (8 x) - ln (x - 3) = ln (x + 3)

ln (10 + x) = ln (3 + 4 x)

2 ln (7 x - 2) - 19 = - 3

lo g_{2} (4 x) - 2 lo g_{2} (5) = 3

ln (3 x) + ln (6) = ln (5 x + 7)

What is the answer to log_{36}(6^a)=a+1 ?
The answer to log_{36}(6^a)=a+1 is a=-2
Solve for a: log_{36}(6^a)=a+1
The solution is a=-2