Change the logarithmic expression to an equivalent expression involving an exponent.
Log1/5(1/625) = C
log(1/5*1/625) = logC,
log(1/3125) = logC,
-3.49 = logC,
logC = -3.49,
10^-3.39 = C,
Or
C = 10^-3.49.
To change a logarithmic expression into an equivalent expression involving an exponent, you need to understand the relationship between logarithms and exponents.
In general, if you have a logarithm in the base b and an exponent x, it can be expressed as:
log base b (x) = y if and only if b^y = x
Now, let's apply this knowledge to the given problem.
The logarithmic expression is: log base 1/5 (1/625) = C
To express it as an equivalent expression involving an exponent:
1/5^C = 1/625
To simplify this further, let's convert 1/5 to its exponent form:
1/5^C = 1/5^(4/625)
Now, we need to eliminate the fraction from the exponent. To do this, we raise both sides to the power of 625:
(1/5^C)^625 = (1/5^(4/625))^625
By applying the exponent rule (a^m)^n = a^(m*n), we get:
1/5^(C*625) = 1/5^(4)
Since the bases on both sides of the equation are the same (5), we can equate the exponents:
C*625 = 4
To isolate C, divide both sides by 625:
C = 4/625
Therefore, the equivalent expression involving an exponent is:
1/5^C = 1/5^(4/625) = 1/5^(4) = 1/625
And the value of C is C = 4/625.