3^2log3(7) show me working step i not using calautor
To simplify the expression 3^2 log3(7), you can use the change of base formula to convert the logarithm from base 3 to base 10. The change of base formula states that logb(x) = loga(x) / loga(b).
Therefore, to convert log3(7) to base 10, divide log(7) by log(3):
log3(7) = log(7) / log(3)
Now, you can substitute this back into the original expression:
3^2 log3(7) = 3^2 * (log(7) / log(3))
Next, evaluate each part of the expression separately:
3^2 = 9
To calculate log(7) / log(3), you can evaluate the logarithms individually and then divide:
log(7) ≈ 0.845
log(3) ≈ 0.477
log(7) / log(3) ≈ 0.845 / 0.477 ≈ 1.770
Finally, substitute these values back into the original expression:
3^2 log3(7) = 9 * 1.770 = 15.930
So, 3^2 log3(7) simplifies to approximately 15.930.