Question

Which equation is equivalent to
log4 + log(x + 2) = 1?

Answer 1

`$x=(1)/(2)$`

Explanation:

If it was not mentioned, the base is 10.

`\log _(10)4+\log _(10)\left(x+2\right)=1`

`\log _(10)4+\log _(10)\left(x+2\right)-\log _(10)4=1-\log _(10)4`

`\log _(10)\left(x+2\right)=1-\log _(10)4`

`\log _(10)\left(x+2\right)=1-2\log _(10)2`

Considering
`\mathrm{if} \log _a\left(b\right)=c\:\mathrm{then}\:b=a^c`

`$x+2=10^{1-2\log _(10)\left2$`

`x+2=10^{-2\log _(10)\left(2\right)}\cdot \:10^1`

`x+2=\left(10^{\log _(10)\left(2\right)}\right)^(-2)\cdot \:10^1`

`x+2=2^(-2)\cdot \:10^1`

`$x+2=10\cdot (1)/(2^2)$`

`$x+2=(10)/(2^2)$`

`$x+2=(5)/(2)$`

`$x+2-2=(5)/(2)-2$`

`$x=(1)/(2)$`

Answer 2

The correct answer is 4x + 8 = 101 on edge 2020. The second part is x=1/2

Explanation: