Datrys 4^-x=3.7

$$4 ^ { - x } = 3.7$$

Datrys ar gyfer x

$$x=\frac{\log_{2}\left(\frac{10}{37}\right)}{2}\approx -0.943762635$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$4^{-x}=3.7$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(4^{-x})=\log(3.7)$$

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

$$-x\log(4)=\log(3.7)$$

Rhannu’r ddwy ochr â \log(4).

$$-x=\frac{\log(3.7)}{\log(4)}$$

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

$$-x=\log_{4}\left(3.7\right)$$

Rhannu’r ddwy ochr â -1.

$$x=\frac{\ln(\frac{37}{10})}{-2\ln(2)}$$

Datrys ar gyfer x (complex solution)

$$x=-\frac{i\pi n_{1}}{\ln(2)}+\frac{\log_{2}\left(\frac{10}{37}\right)}{2}$$

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