Datrys {left(7/8right)}^2x+3=2

$${ \left( \frac{ 7 }{ 8 } \right) }^{ 2x+3 } =2$$

Datrys ar gyfer x

$$x = -\frac{\log_{\frac{7}{8}} {(\frac{343}{1024})}}{2} \approx -4.095446535$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$\left(\frac{7}{8}\right)^{2x+3}=2$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(\left(\frac{7}{8}\right)^{2x+3})=\log(2)$$

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

$$\left(2x+3\right)\log(\frac{7}{8})=\log(2)$$

Rhannu’r ddwy ochr â \log(\frac{7}{8}).

$$2x+3=\frac{\log(2)}{\log(\frac{7}{8})}$$

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

$$2x+3=\log_{\frac{7}{8}}\left(2\right)$$

Tynnu 3 o ddwy ochr yr hafaliad.

$$2x=\frac{\ln(2)}{\ln(\frac{7}{8})}-3$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{\frac{\ln(2)}{\ln(\frac{7}{8})}-3}{2}$$