Explanation:
To solve exponential equations we have to use the properties of the logarithms:
[tex]2^x=3[/tex]First we apply log on both sides of the equation:
[tex]\log (2^x)=\log (3)[/tex]Now we use the logarithm of a power property:
[tex]\log (a^b)=b\log (a)[/tex]For this equation:
[tex]x\log (2)=\log (3)[/tex]And divide both sides by log(2):
[tex]x=\frac{\log (3)}{\log (2)}\approx1.585[/tex]Anwers:
• (a) ,x = log(3)/log(2)
,• (b) ,x = 1.585
