Question

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

Answer 1

Answer:

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

Step-by-step explanation:

given,

log₂ (800)

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,                                    

log₂ (800)                    

log₂ (2³ × 100 )                          

log₂ (2³) + log₂ (100)                    

3 log₂ (2) + log₂ (10²)                      

3 + 2 log₂ (10)                              

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