Datrys 15^3x-4=10

$$15 ^ { 3 x - 4 } = 10$$

Datrys ar gyfer x

$$x = \frac{\log_{15} {(506250)}}{3} \approx 1.616758051$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$15^{3x-4}=10$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(15^{3x-4})=\log(10)$$

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

$$\left(3x-4\right)\log(15)=\log(10)$$

Rhannu’r ddwy ochr â \log(15).

$$3x-4=\frac{\log(10)}{\log(15)}$$

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

$$3x-4=\log_{15}\left(10\right)$$

Adio 4 at ddwy ochr yr hafaliad.

$$3x=\log_{15}\left(10\right)-\left(-4\right)$$

Rhannu’r ddwy ochr â 3.

$$x=\frac{\log_{15}\left(10\right)+4}{3}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(15)}+\frac{\log_{15}\left(506250\right)}{3}$$

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