Question

Rewrite each expression in an equivalent form that only contains one base 10 logarithm.

Answer 1

Answer:

$3 + \dfrac{2}{log_{10}5}$

Step-by-step explanation:

given,

log₅ (12500)

using logarithmic identity

logₐ a = 1                              

logₐ x³ = 3 logₐ x                    

log (ab) = log a + log b            

logₐ x = $\dfrac{1}{log_x a}$

now,                                    

log₅ (12500)                    

log₅ (5³ × 100 )                          

log₅ (5³) + log₅(100)                    

3 log₅ (5) + log₅ (10²)                      

3 + 2 log₅ (10)                              

$3 + \dfrac{2}{log_{10}5}$

hence, the required solution is given above.