What is the answer to log_{2}(5x)-log_{2}(x-3)=4 ?

The answer to log_{2}(5x)-log_{2}(x-3)=4 is x= 48/11

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log_{2}(5x)-log_{2}(x-3)=4

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

x = \frac{48}{11}

Decimal Notation

x = 4.36363 \dots

Solution steps

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

Add

lo g_{2} (x - 3)

to both sides

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

Simplify

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

Apply log rules

5 x = 16 (x - 3)

Solve

5 x = 16 (x - 3) : x = \frac{48}{11}

x = \frac{48}{11}

Verify Solutions:

x = \frac{48}{11}

True

The solution is

x = \frac{48}{11}

lo g_{10} (x) = 1.4

\frac{ln ( x - 10 )}{e} = x - 10

ln (x) = 5.208050342

lo g_{4} (x + 7) - lo g_{4} (x) = 3

lo g_{4} (16) + lo g_{4} (2 x + 9) = 3

What is the answer to log_{2}(5x)-log_{2}(x-3)=4 ?
The answer to log_{2}(5x)-log_{2}(x-3)=4 is x= 48/11
Solve for x: log_{2}(5x)-log_{2}(x-3)=4
The solution is x= 48/11