The required value of x for the given equation is about 1.71.
Equation:
Important information:
- The given equation is [tex]10(1.5)^{3x}=80[/tex].
Divide both sides by 10.
[tex](1.5)^{3x}=\dfrac{80}{10}[/tex]
[tex](1.5)^{3x}=8[/tex]
Taking log on both sides, we get
[tex]\log (1.5)^{3x}=\log 2^3[/tex]
[tex]3x\log (1.5)=3\log 2[/tex]
Divide both sides by 3log(1.5).
[tex]x=\dfrac{3\log 2}{3\log 1.5}[/tex]
[tex]x=\dfrac{\log 2}{\log 1.5}[/tex]
[tex]x\approx 1.71[/tex]
Therefore, the required value of x for the given equation is about 1.71.
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