Question

logbase7(a) * logbaseb(7)
Which of the following are equivalent
A. Log(7)
B. Log(7a)
C. Logbasea(b)
D. Logbaseb(a)

Answer 1

Answer:

D

Step-by-step explanation:

We have $(log_7a)*(log_b7)$. Remember the logarithm properties to turn this into log base 10. For a logarithm $log_ba$, it is equivalent to $\frac{log(a)}{log(b)}$.

So:

$(log_7a)*(log_b7)=\frac{log(a)}{log(7)} *\frac{log(7)}{log(b)}$

The log(7) cancel out and we're left with:

$\frac{log(a)}{log(b)}$

We can now work backwards and turn this into one logarithm. Since before, we had $log_ba$ ⇒ $\frac{log(a)}{log(b)}$, we now have $\frac{log(a)}{log(b)}$ ⇒ $log_ba$.

Thus, the answer is D.

Hope this helps!

Answer 2

Answer:

D

Step-by-step explanation:

log7(a) × logb(7)

Using change of base law, let's convert all of them into lg

lg(a)/lg(7) × lg(7)/lg(b)

lg(a)/lg(b)

Again, using change of base law we can convert this into:

logb(a)