Question

Solve each exponential equation by using properties of common logarithms. Do not round the expression until the final answer. When necessary, round answers to the nearest hundredth.

17x = 89

x ≈ 1.58
x ≈ 5.24
x ≈ 63

Answer 1

The answer is x 1.45

Answer 2

Option 1 -
`x\approx 1.58`

Explanation:

Given : Exponential equation
`17^x=89`

To find : Solve exponential equation by using properties of common logarithms?

Solution :

Step 1 - Write the exponential equation,

`17^x=89`

Step 2 - Take logarithm both side,

`\log 17^x=\log 89`

Step 3 - Apply logarithmic property,
`\log a^x=x\log a`

`x\log 17=\log 89`

Step 4 - Divide both side by log 17,

`x=(\log 89)/(\log 17)`

Step 5 - Solve,

`x=1.584`

`x\approx 1.58`

Therefore, Option 1 is correct.