Datrys 2.400/1200=(109/100)^x

$$\frac { 2.400 } { 1200 } = ( \frac { 109 } { 100 } ) ^ { x }$$

Datrys ar gyfer x

$$x=-\log_{1.09}\left(500\right)\approx -72.113880615$$

Camau gan Ddefnyddio Diffiniad Logarithm

Ehangu \frac{2.4}{1200} drwy luosi'r rhifiadur a'r enwadur gyda 10.

$$\frac{24}{12000}=\left(\frac{109}{100}\right)^{x}$$

Lleihau'r ffracsiwn \frac{24}{12000} i'r graddau lleiaf posib drwy dynnu a chanslo allan 24.

$$\frac{1}{500}=\left(\frac{109}{100}\right)^{x}$$

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

$$\left(\frac{109}{100}\right)^{x}=\frac{1}{500}$$

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$\left(\frac{109}{100}\right)^{x}=0.002$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(\left(\frac{109}{100}\right)^{x})=\log(0.002)$$

Logarithm rhif wedi’i godi i bŵer yw’r pŵer wedi’i lluosi â logarithm y rhif.

$$x\log(\frac{109}{100})=\log(0.002)$$

Rhannu’r ddwy ochr â \log(\frac{109}{100}).

$$x=\frac{\log(0.002)}{\log(\frac{109}{100})}$$

Gyda’r fformiwla newid-sail \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$x=\log_{\frac{109}{100}}\left(0.002\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.09)}-\log_{1.09}\left(500\right)$$

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