Answer:
[tex]x=2.5[/tex]
Step-by-step explanation:
We have,
[tex]4x+2=12[/tex]
[tex]\implies4x=10[/tex]
Taking log both the sides we have,
[tex]log\,4x=log\,10[/tex]
[tex]\implies log\,4 + log\,x=log\,10 \left\:\: [ \because log\,ab = log\, a + log\, b\right ][/tex]
[tex]\implies log\,x=log\,10 -log\,4[/tex]
[tex]\implies log\,x={ log\,(\frac{10}{4}) \:\:\left [\because log\,a -log\,b= log\,\frac{a}{b} \right ][/tex]
[tex]\implies log\,x=log\,2.5[/tex]
[tex]\implies \frac{log\,x}{log\,2.5}=1[/tex]
[tex]\implies log_{(2.5)}\, x=1\:\:\left [ \because log_{b}\,a=\frac{log\,a}{log\,b} \right ][/tex]
[tex]\implies x=(2.5)^{1}\:\: [ \because log_{b}\,a=m \implies a=b^{m} ][/tex]
Hence, we have [tex]x=2.5[/tex]
