What is the answer to log_{5}(4t+7)-log_{5}(t)=2 ?

The answer to log_{5}(4t+7)-log_{5}(t)=2 is t= 1/3

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log_{5}(4t+7)-log_{5}(t)=2

lo g_{5} (4 t + 7) - lo g_{5} (t) = 2

t = \frac{1}{3}

Solution steps

lo g_{5} (4 t + 7) - lo g_{5} (t) = 2

Add

lo g_{5} (t)

to both sides

lo g_{5} (4 t + 7) - lo g_{5} (t) + lo g_{5} (t) = 2 + lo g_{5} (t)

Simplify

lo g_{5} (4 t + 7) = 2 + lo g_{5} (t)

Apply log rules

4 t + 7 = 25 t

Solve

4 t + 7 = 25 t : t = \frac{1}{3}

t = \frac{1}{3}

Verify Solutions:

t = \frac{1}{3}

True

The solution is

t = \frac{1}{3}

- lo g_{3} (x) + 2 = 0

10 = lo g_{2} (x)

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

lo g_{\frac{2}{5}} (x) = 0

6 - 3 lo g_{10} (2 n) = 0

What is the answer to log_{5}(4t+7)-log_{5}(t)=2 ?
The answer to log_{5}(4t+7)-log_{5}(t)=2 is t= 1/3
Solve for t: log_{5}(4t+7)-log_{5}(t)=2
The solution is t= 1/3