Respuesta :
Answer:
Option 1 - [tex]x\approx 1.58[/tex]
Step-by-step explanation:
Given : Exponential equation [tex]17^x=89[/tex]
To find : Solve exponential equation by using properties of common logarithms?
Solution :
Step 1 - Write the exponential equation,
[tex]17^x=89[/tex]
Step 2 - Take logarithm both side,
[tex]\log 17^x=\log 89[/tex]
Step 3 - Apply logarithmic property, [tex]\log a^x=x\log a[/tex]
[tex]x\log 17=\log 89[/tex]
Step 4 - Divide both side by log 17,
[tex]x=\frac{\log 89}{\log 17}[/tex]
Step 5 - Solve,
[tex]x=1.584[/tex]
[tex]x\approx 1.58[/tex]
Therefore, Option 1 is correct.
