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

Answer:

Option 1 - $x\approx 1.58$

Step-by-step 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,

$x=\frac{\log 89}{\log 17}$

Step 5 - Solve,

$x=1.584$

$x\approx 1.58$

Therefore, Option 1 is correct.

Answer 2

The answer is x 1.45