Datrys 4+5*7^x=16+2*7^x

$$4 + 5 \cdot 7 ^ { x } = 16 + 2 \cdot 7 ^ { x }$$

Datrys ar gyfer x

$$x=2\log_{7}\left(2\right)\approx 0.712414374$$

Camau gan Ddefnyddio Diffiniad Logarithm

Tynnu 2\times 7^{x} o'r ddwy ochr.

$$4+5\times 7^{x}-2\times 7^{x}=16$$

Cyfuno 5\times 7^{x} a -2\times 7^{x} i gael 3\times 7^{x}.

$$4+3\times 7^{x}=16$$

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3\times 7^{x}+4=16$$

Tynnu 4 o ddwy ochr yr hafaliad.

$$3\times 7^{x}=12$$

Rhannu’r ddwy ochr â 3.

$$7^{x}=4$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(7^{x})=\log(4)$$

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

$$x\log(7)=\log(4)$$

Rhannu’r ddwy ochr â \log(7).

$$x=\frac{\log(4)}{\log(7)}$$

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

$$x=\log_{7}\left(4\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(7)}+2\log_{7}\left(2\right)$$

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