What is log_{1/2}(8/15) ?

The solution to log_{1/2}(8/15) is -3+log_{2}(15)

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simplify log_{1/2}(8/15)

simplify

lo g_{\frac{1}{2}} (\frac{8}{15})

- 3 + lo g_{2} (15)

Decimal Notation

0.90689 \dots

Solution steps

lo g_{\frac{1}{2}} (\frac{8}{15})

Apply log rule:

lo g_{\frac{1}{a}} (x) = - lo g_{a} (x)

lo g_{\frac{1}{2}} (\frac{8}{15}) = - lo g_{2} (\frac{8}{15})

= - lo g_{2} (\frac{8}{15})

Apply log rule:

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

lo g_{2} (\frac{8}{15}) = lo g_{2} (8) - lo g_{2} (15)

= - (lo g_{2} (8) - lo g_{2} (15))

lo g_{2} (8) = 3

= - (3 - lo g_{2} (15))

Apply the distributive law:

- (a - b) = - a + b

- (3 - lo g_{2} (15)) = - 3 + lo g_{2} (15)

= - 3 + lo g_{2} (15)

5 ln (x) + 4 ln (y) - 3 ln (z)

lo g_{6} ((\frac{x}{216})^{4})

\frac{ln ( 2.5 ) - ln ( 2.2 )}{2.5 - 2.2}