What is ln(4.98*10^{15}*e^{0.47(2000-2010)}) ?

The solution to ln(4.98*10^{15}*e^{0.47(2000-2010)}) is ln(4.98)+15ln(10)-4.7

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simplify ln(4.9810^{15}e^{0.47(2000-2010)})

simplify

ln (4.98 \cdot 1 0^{15} \cdot e^{0.47 (2000 - 2010)})

ln (4.98) + 15 ln (10) - 4.7

Decimal Notation

31.44420 \dots

Solution steps

ln (4.98 \cdot 1 0^{15} e^{0.47 (2000 - 2010)})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (4.98 \cdot 1 0^{15} e^{0.47 (2000 - 2010)}) = ln (4.98) + ln (1 0^{15}) + ln (e^{0.47 (2000 - 2010)})

= ln (4.98) + ln (1 0^{15}) + ln (e^{0.47 (2000 - 2010)})

Apply log rule:

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

ln (1 0^{15}) = 15 ln (10)

= ln (4.98) + 15 ln (10) + ln (e^{0.47 (2000 - 2010)})

Apply log rule:

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

ln (e^{0.47 (2000 - 2010)}) = 0.47 (2000 - 2010) ln (e)

= ln (4.98) + 15 ln (10) + 0.47 (2000 - 2010) ln (e)

0.47 (2000 - 2010) ln (e) = - 4.7

= ln (4.98) + 15 ln (10) - 4.7

lo g_{10} (6) lo g_{10} (2) + lo g_{10} (3)

(\frac{1}{0.143}) ln (\frac{6 \cdot 1 0 ^{9}}{29000})

ln (\frac{547}{273}) \cdot 8

lo g_{0.3} (10) - lo g_{0.3} (3)

\frac{3}{4} lo g_{10} (7 + 43)

What is ln(4.98*10^{15}*e^{0.47(2000-2010)}) ?
The solution to ln(4.98*10^{15}*e^{0.47(2000-2010)}) is ln(4.98)+15ln(10)-4.7