Solve 9.8=149/15e^-frac{0.1{45}x}

$$9.8 = \frac { 149 } { 15 } e ^ { - \frac { 0.1 } { 45 } x }$$

Solve for x

$$x=\ln(\frac{858659117050020499497940039808644067081004050825944207953853227966193131123237600680234061466031975798956042974091067536374298755860100838381167459000407947107220911954610960085868559116877351817048892164983257529318108993477740859117016119239722074577716865924518936288956308415123322298264700657298693482712485094777339947412950125012022880859381614979372291430360033400616567443990085520118150771512197106500676662709405383083132175857731142220699600000356155852903950409347451700769355114307325511964919303626754391446082414259270177373478577009555928605794276920777968920453634647811564198195233239434706461493204758663822089577053366221234288232427378033039399213681115829099624599399041906818437876430391452924431775441269833643250580583020157407938121748880824598190822577728466391552101346634428041687440470240831979696772199475777058694592213337354515537126250375886061641386676634236708289622951132315286592969581233208256480282770287490320194720093696784493172995001}{1962459201152739958702534936363704010756007219330606188922234275609301713510172005803039590292541747509803505306278637998255286446607212583823688197987365459205737586212984895809210672110368049416704052878701540785984036427996810438406921579859341966087216519696381332740156213750133571699747222232227191333472770377717673169028589175844353711587033328297355407096209042744098738120483554378825655398354824259900253659756323767508751226753154922172141797660823568237109458901773705132134782784526045224785607741141593064546866751019349221599205832977603157275736671290504357666330014631151274979522678296963611925061064522381250444487708986393016048674077111289691591305428463127229549011015882622552923863542495705376676123082991182358872586360839678874919717006581923831488955620051860500076160536323130464502226364162361075778378689122221647106800187757236446972239401535759776545406220876003159637515355686947632561084747197807966629193334224685988318629744971132999142249})$$

Steps Using Definition of Logarithm

Multiply both sides by \frac{15}{149}, the reciprocal of \frac{149}{15}.

$$9.8\times \frac{15}{149}=e^{\left(-\frac{0.1}{45}\right)x}$$

Multiply 9.8 and \frac{15}{149} to get \frac{147}{149}.

$$\frac{147}{149}=e^{\left(-\frac{0.1}{45}\right)x}$$

Expand \frac{0.1}{45} by multiplying both numerator and the denominator by 10.

$$\frac{147}{149}=e^{-\frac{1}{450}x}$$

Swap sides so that all variable terms are on the left hand side.

$$e^{-\frac{1}{450}x}=\frac{147}{149}$$

Take the logarithm of both sides of the equation.

$$\log(e^{-\frac{1}{450}x})=\log(\frac{147}{149})$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$-\frac{1}{450}x\log(e)=\log(\frac{147}{149})$$

Divide both sides by \log(e).

$$-\frac{1}{450}x=\frac{\log(\frac{147}{149})}{\log(e)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$-\frac{1}{450}x=\log_{e}\left(\frac{147}{149}\right)$$

Multiply both sides by -450.

$$x=\frac{\ln(\frac{147}{149})}{-\frac{1}{450}}$$

Solve for x (complex solution)

$$x=-i\times 900\pi n_{1}+\ln(\frac{858659117050020499497940039808644067081004050825944207953853227966193131123237600680234061466031975798956042974091067536374298755860100838381167459000407947107220911954610960085868559116877351817048892164983257529318108993477740859117016119239722074577716865924518936288956308415123322298264700657298693482712485094777339947412950125012022880859381614979372291430360033400616567443990085520118150771512197106500676662709405383083132175857731142220699600000356155852903950409347451700769355114307325511964919303626754391446082414259270177373478577009555928605794276920777968920453634647811564198195233239434706461493204758663822089577053366221234288232427378033039399213681115829099624599399041906818437876430391452924431775441269833643250580583020157407938121748880824598190822577728466391552101346634428041687440470240831979696772199475777058694592213337354515537126250375886061641386676634236708289622951132315286592969581233208256480282770287490320194720093696784493172995001}{1962459201152739958702534936363704010756007219330606188922234275609301713510172005803039590292541747509803505306278637998255286446607212583823688197987365459205737586212984895809210672110368049416704052878701540785984036427996810438406921579859341966087216519696381332740156213750133571699747222232227191333472770377717673169028589175844353711587033328297355407096209042744098738120483554378825655398354824259900253659756323767508751226753154922172141797660823568237109458901773705132134782784526045224785607741141593064546866751019349221599205832977603157275736671290504357666330014631151274979522678296963611925061064522381250444487708986393016048674077111289691591305428463127229549011015882622552923863542495705376676123082991182358872586360839678874919717006581923831488955620051860500076160536323130464502226364162361075778378689122221647106800187757236446972239401535759776545406220876003159637515355686947632561084747197807966629193334224685988318629744971132999142249})$$

$$n_{1}\in \mathrm{Z}$$