What is the answer to log_{10}(16-x^2)-log_{10}(3x-4)=2 ?

The answer to log_{10}(16-x^2)-log_{10}(3x-4)=2 is x=2(sqrt(5729)-75)

Solve for x: log_{10}(16-x^2)-log_{10}(3x-4)=2

The solution is x=2(sqrt(5729)-75)

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lo g_{10} (16 - x^{2}) - lo g_{10} (3 x - 4) = 2

x = 2 (5729 - 75)

Decimal Notation

x = 1.38031 \dots

Solution steps

lo g_{10} (16 - x^{2}) - lo g_{10} (3 x - 4) = 2

Add

lo g_{10} (3 x - 4)

to both sides

lo g_{10} (16 - x^{2}) - lo g_{10} (3 x - 4) + lo g_{10} (3 x - 4) = 2 + lo g_{10} (3 x - 4)

Simplify

lo g_{10} (16 - x^{2}) = 2 + lo g_{10} (3 x - 4)

Apply log rules

16 - x^{2} = 100 (3 x - 4)

Solve

16 - x^{2} = 100 (3 x - 4) : x = - 2 (75 + 5729), x = 2 (5729 - 75)

x = - 2 (75 + 5729), x = 2 (5729 - 75)

Verify Solutions:

x = - 2 (75 + 5729)

False

, x = 2 (5729 - 75)

True

The solution is

x = 2 (5729 - 75)

lo g_{10} (x^{2} + 3) = lo g_{10} (x + 6)

a, lo g_{2} (a^{3}) + lo g_{2} (b) = 8

lo g_{5} (x^{5} + x - 1) = 5

2 lo g_{10} (x) = 4

lo g_{3} ((x + 2)^{2}) + 1 = 7

What is the answer to log_{10}(16-x^2)-log_{10}(3x-4)=2 ?
The answer to log_{10}(16-x^2)-log_{10}(3x-4)=2 is x=2(sqrt(5729)-75)
Solve for x: log_{10}(16-x^2)-log_{10}(3x-4)=2
The solution is x=2(sqrt(5729)-75)