What is the domain of f(x)=log_{10}(3x+9)+log_{10}(x+8) ?

The domain of f(x)=log_{10}(3x+9)+log_{10}(x+8) is x>-3

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domain of f(x)=log_{10}(3x+9)+log_{10}(x+8)

domain

f (x) = lo g_{10} (3 x + 9) + lo g_{10} (x + 8)

x > - 3

Interval Notation

(- 3, \infty)

Solution steps

Find positive values for logs:

x > - 3

The function domain

x > - 3

f (x) = lo g_{\frac{1}{3}} (3 x)

ln (5) - ln (20)

10 lo g_{10} (2) + lo g_{10} (3) - 3 lo g_{10} (4)

- \frac{6}{11} lo g_{2} (\frac{6}{11}) - \frac{5}{11} lo g_{2} (\frac{5}{11})

lo g_{5} (\frac{25}{x + 4})

What is the domain of f(x)=log_{10}(3x+9)+log_{10}(x+8) ?
The domain of f(x)=log_{10}(3x+9)+log_{10}(x+8) is x>-3