What is the answer to log_{2}(x)=3-log_{2}(3x-10) ?

The answer to log_{2}(x)=3-log_{2}(3x-10) is x=4

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log_{2}(x)=3-log_{2}(3x-10)

lo g_{2} (x) = 3 - lo g_{2} (3 x - 10)

x = 4

Solution steps

lo g_{2} (x) = 3 - lo g_{2} (3 x - 10)

Add

lo g_{2} (3 x - 10)

to both sides

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

Simplify

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

Apply log rules

x (3 x - 10) = 8

Solve

x (3 x - 10) = 8 : x = 4, x = - \frac{2}{3}

x = 4, x = - \frac{2}{3}

Verify Solutions:

x = 4

True

, x = - \frac{2}{3}

False

The solution is

x = 4

lo g_{e} (\frac{760}{x}) = 751

lo g_{4} (x^{2} + 3) = 2

lo g_{b} (343) = - \frac{3}{2}

lo g_{a} (64) = 2

lo g_{9} (2 x - 7) = \frac{3}{2}

What is the answer to log_{2}(x)=3-log_{2}(3x-10) ?
The answer to log_{2}(x)=3-log_{2}(3x-10) is x=4
Solve for x: log_{2}(x)=3-log_{2}(3x-10)
The solution is x=4