What is the answer to log_{10}(15-2)=2log_{10}(x) ?

The answer to log_{10}(15-2)=2log_{10}(x) is x=10^{(log_{10}(13))/2}

Solve for x: log_{10}(15-2)=2log_{10}(x)

The solution is x=10^{(log_{10}(13))/2}

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lo g_{10} (15 - 2) = 2 lo g_{10} (x)

x = 1 0^{\frac{l o g _{10} ( 13 )}{2}}

Decimal Notation

x = 3.60555 \dots

Solution steps

lo g_{10} (15 - 2) = 2 lo g_{10} (x)

Switch sides

2 lo g_{10} (x) = lo g_{10} (15 - 2)

Divide both sides by

2

lo g_{10} (x) = \frac{lo g _{10} ( 15 - 2 )}{2}

Simplify

lo g_{10} (x) = \frac{lo g _{10} ( 13 )}{2}

Apply log rules

x = 1 0^{\frac{l o g _{10} ( 13 )}{2}}

Verify Solutions:

x = 1 0^{\frac{l o g _{10} ( 13 )}{2}}

True

The solution is

x = 1 0^{\frac{l o g _{10} ( 13 )}{2}}

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

lo g_{10} (2 x - 6) = lo g_{10} (6 - x)

ln (x^{3} + 19) = 3 ln (x + 1)

- 2 lo g_{5} (2 b + 7) = 9

lo g_{4} (5 x - 6) = 4

What is the answer to log_{10}(15-2)=2log_{10}(x) ?
The answer to log_{10}(15-2)=2log_{10}(x) is x=10^{(log_{10}(13))/2}
Solve for x: log_{10}(15-2)=2log_{10}(x)
The solution is x=10^{(log_{10}(13))/2}