Can you please tell me me if the expression or equation that is equivant to 8^x=3 would be x log 3 = log 8?
Actually,
x log8 = log 3, but what they probably want is
log(base8)3 = x
In any case, x = 0.52832
My choices for this question are
a x = log8 over log 3
b x log = log 8
c x=log 3 over log 8
d x= ln8 over ln3
My choices for this question are
a x = log8 over log 3
b x log = log 8
c x=log 3 over log 8
d x= ln8 over ln3
Yes, the expression x log 3 = log 8 is equivalent to the equation 8^x = 3. Let me explain why:
Starting with the equation 8^x = 3, we want to find an equivalent expression that involves logarithms.
To do that, we can take the logarithm of both sides of the equation. The choice of logarithm base is arbitrary, but let's use the common logarithm (base 10) for this explanation.
Applying the logarithm to both sides, we get:
log(8^x) = log(3)
According to the logarithmic property, the exponent x can be brought down as a coefficient in front of the logarithm:
x log(8) = log(3)
Now, notice that on the right side of the equation, we have log(3), while on the left side, we have x log(8).
So, yes, the expression x log 3 = log 8 is equivalent to the equation 8^x = 3.