What is the answer to 6log_{10}(a)+6log_{10}(a-9)=2 ?

The answer to 6log_{10}(a)+6log_{10}(a-9)=2 is a\approx 9.23333…

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6log_{10}(a)+6log_{10}(a-9)=2

6 lo g_{10} (a) + 6 lo g_{10} (a - 9) = 2

a \approx 9.23333 \dots

Solution steps

6 lo g_{10} (a) + 6 lo g_{10} (a - 9) = 2

Divide both sides by

2

\frac{6 lo g _{10} ( a )}{2} + \frac{6 lo g _{10} ( a - 9 )}{2} = \frac{2}{2}

Simplify

3 lo g_{10} (a) + 3 lo g_{10} (a - 9) = 1

Apply log rules

a^{3} (a - 9)^{3} = 10

Solve

a^{3} (a - 9)^{3} = 10 : a \approx - 0.23333 \dots, a \approx 9.23333 \dots

a \approx - 0.23333 \dots, a \approx 9.23333 \dots

Verify Solutions:

a \approx - 0.23333 \dots

False

, a \approx 9.23333 \dots

True

The solution is

a \approx 9.23333 \dots

ln (x - 1) - ln (x + 2) = ln (2)

a lo g_{2} (3.5) = lo g_{27} (- lo g_{22} (x))

x - 7 + lo g_{2} (x + 8) = - 5

ln (2) - ln (3 x + 4) + ln (4 - 3 x) = ln (2)

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

What is the answer to 6log_{10}(a)+6log_{10}(a-9)=2 ?
The answer to 6log_{10}(a)+6log_{10}(a-9)=2 is a\approx 9.23333…
Solve for a: 6log_{10}(a)+6log_{10}(a-9)=2
The solution is a\approx 9.23333…