given that loga 16 - loga 8=1 find a a). 4 b). 2 c). 10 d). 5?
loga 16 - loga 8=1
loga(16/8) = 1
loga 2 = 1
use your definition of logs to find a, do it mentally.
To solve the equation loga 16 - loga 8 = 1, we can use the logarithmic property that states loga(x) - loga(y) = loga(x/y). Applying this property, we have:
loga 16 - loga 8 = loga(16/8)
Simplifying further, we have:
loga(16/8) = loga(2)
Now, to find the value of 'a', we need to solve the equation loga(2) = 1.
In logarithmic form, this equation can be written as:
a^1 = 2
So, 'a' needs to be a number that, when raised to the power of 1, gives us 2. The options given are:
a) 4
b) 2
c) 10
d) 5
To find the correct answer, simply substitute the different options for 'a' in the equation a^1 = 2 and see which one satisfies it:
a) 4^1 = 4 ≠2 (not correct)
b) 2^1 = 2 (correct)
c) 10^1 = 10 ≠2 (not correct)
d) 5^1 = 5 ≠2 (not correct)
Therefore, the correct answer is b) 2.