What is log_{7}((sqrt(h-3))/(49)) ?

The solution to log_{7}((sqrt(h-3))/(49)) is log_{7}(sqrt(h-3))-2

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simplify log_{7}((sqrt(h-3))/(49))

simplify

lo g_{7} (\frac{h - 3}{49})

lo g_{7} (h - 3) - 2

Solution steps

lo g_{7} (\frac{h - 3}{49})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{7} (\frac{h - 3}{49}) = lo g_{7} (h - 3) - lo g_{7} (49)

= lo g_{7} (h - 3) - lo g_{7} (49)

lo g_{7} (49) = 2

= lo g_{7} (h - 3) - 2

\frac{1}{2} ln (x) + 3 ln (y) - 2 ln (x)

lo g_{4} (u) + 6 lo g_{4} (v) + 3 lo g_{4} (w)

\frac{1}{2} lo g_{10} (x) + 6 lo g_{10} (y)

\frac{1}{3} (ln (\frac{x}{3} + 1) - ln (\frac{x}{3} - 1))

- (\frac{3}{14}) lo g_{2} (\frac{3}{14}) - (\frac{2}{14}) lo g_{2} (\frac{2}{14})

What is log_{7}((sqrt(h-3))/(49)) ?
The solution to log_{7}((sqrt(h-3))/(49)) is log_{7}(sqrt(h-3))-2