Answer :
To solve the equation [tex]3 + 7 \cdot \log_5 x = 25[/tex], we will follow the steps below:
Subtract 3 from both sides:
Start by isolating the logarithmic part:
[tex]7 \cdot \log_5 x = 25 - 3[/tex]
[tex]7 \cdot \log_5 x = 22[/tex]Divide both sides by 7:
Isolate the logarithm completely by dividing both sides by 7:
[tex]\log_5 x = \frac{22}{7}[/tex]Convert the logarithmic equation to an exponential equation:
Recall that [tex]\log_b a = c[/tex] means [tex]b^c = a[/tex]. Therefore, [tex]5^{\frac{22}{7}} = x[/tex].
Calculate [tex]x[/tex]:
Use a calculator to find [tex]x[/tex] by evaluating [tex]5^{\frac{22}{7}}[/tex]:
[tex]x \approx 369.33[/tex]
Hence, the solution to the equation is [tex]x = 369.33[/tex].
Therefore, the correct multiple-choice option is A. x = 369.33.