What is 0.56+0.027*ln((10^{16})/(1.5*10^{10)}) ?

The solution to 0.56+0.027*ln((10^{16})/(1.5*10^{10)}) is 0.56+0.027(16ln(10)-ln(1.5*10^{10}))

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simplify 0.56+0.027ln((10^{16})/(1.510^{10)})

simplify

0.56 + 0.027 \cdot ln (\frac{1 0 ^{16}}{1.5 \cdot 1 0 ^{10}})

0.56 + 0.027 (16 ln (10) - ln (1.5 \cdot 1 0^{10}))

Decimal Notation

0.92207 \dots

Solution steps

0.56 + 0.027 ln (\frac{1 0 ^{16}}{1.5 \cdot 1 0 ^{10}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{1 0 ^{16}}{1.5 \cdot 1 0 ^{10}}) = ln (1 0^{16}) - ln (1.5 \cdot 1 0^{10})

= 0.56 + 0.027 (ln (1 0^{16}) - ln (1 0^{10} \cdot 1.5))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (1 0^{16}) = 16 ln (10)

= 0.56 + 0.027 (16 ln (10) - ln (1.5 \cdot 1 0^{10}))

- \frac{4}{13} lo g_{2} (\frac{4}{13}) - \frac{9}{13} lo g_{2} (\frac{9}{13})

lo g_{10} (\frac{x}{z ^{5} y})

lo g_{3} (\frac{1}{( x ^{2} y 3 ^{z} )})

ln (\frac{( 6 + 0 )}{4 - 0})

\frac{4 ln ( 2 )}{ln ( \frac{25}{24} )}

What is 0.56+0.027*ln((10^{16})/(1.5*10^{10)}) ?
The solution to 0.56+0.027*ln((10^{16})/(1.5*10^{10)}) is 0.56+0.027(16ln(10)-ln(1.5*10^{10}))