What is the answer to log_{10}(sqrt(3x+1))-log_{10}(sqrt(2x-3))=1-log_{10}(5) ?

The answer to log_{10}(sqrt(3x+1))-log_{10}(sqrt(2x-3))=1-log_{10}(5) is x= 13/5

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log_{10}(sqrt(3x+1))-log_{10}(sqrt(2x-3))=1-log_{10}(5)

lo g_{10} (3 x + 1) - lo g_{10} (2 x - 3) = 1 - lo g_{10} (5)

x = \frac{13}{5}

Decimal

x = 2.6

Solution steps

lo g_{10} (3 x + 1) - lo g_{10} (2 x - 3) = 1 - lo g_{10} (5)

Add

lo g_{10} (2 x - 3)

to both sides

lo g_{10} (3 x + 1) - lo g_{10} (2 x - 3) + lo g_{10} (2 x - 3) = 1 - lo g_{10} (5) + lo g_{10} (2 x - 3)

Simplify

lo g_{10} (3 x + 1) = 1 - lo g_{10} (5) + lo g_{10} (2 x - 3)

Add

lo g_{10} (5)

to both sides

lo g_{10} (3 x + 1) + lo g_{10} (5) = 1 - lo g_{10} (5) + lo g_{10} (2 x - 3) + lo g_{10} (5)

Simplify

lo g_{10} (3 x + 1) + lo g_{10} (5) = lo g_{10} (2 x - 3) + 1

Apply log rules

3 x + 1 \cdot 5 = 2 x - 3 \cdot 10

Solve

3 x + 1 \cdot 5 = 2 x - 3 \cdot 10 : x = \frac{13}{5}

x = \frac{13}{5}

Verify Solutions:

x = \frac{13}{5}

True

The solution is

x = \frac{13}{5}

5 x^{4} ln (x) + x^{4} = 0

\frac{ln ( 6 b )}{6} = 0

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

lo g_{12} (2 x - 6) + 3 = 3

ln (x) = 9.353416701

What is the answer to log_{10}(sqrt(3x+1))-log_{10}(sqrt(2x-3))=1-log_{10}(5) ?
The answer to log_{10}(sqrt(3x+1))-log_{10}(sqrt(2x-3))=1-log_{10}(5) is x= 13/5
Solve for x: log_{10}(sqrt(3x+1))-log_{10}(sqrt(2x-3))=1-log_{10}(5)
The solution is x= 13/5