solve for x from (0.008)^x=1/25 i'm confuse help me
(0.008)^x = 1/25.
Take log of both sides:
X*log(0.008) = log(0.04),
-2.0969*X = -1.3979,
X = -1.3979 / -2.0969 = 0.6667.
To solve for x in the equation (0.008)^x = 1/25, we can use logarithms. Specifically, we can take the logarithm of both sides of the equation to eliminate the exponent and solve for x.
Let's begin by taking the logarithm of both sides. Since the base in the equation is not specified, we can use the natural logarithm (ln) or the common logarithm (log). Here, we'll use the natural logarithm:
ln((0.008)^x) = ln(1/25)
Now, we can apply the logarithm property, which states that the logarithm of a power is equal to the exponent multiplied by the logarithm of the base:
x * ln(0.008) = ln(1/25)
Next, we need to evaluate the natural logarithms on both sides of the equation. We can use a calculator or a logarithm table to find the values of ln(0.008) and ln(1/25).
Using a calculator, we find that ln(0.008) ≈ -4.8283 and ln(1/25) ≈ -3.2189. Plugging in these values into the equation:
x * -4.8283 = -3.2189
Simplifying further:
-4.8283x = -3.2189
To isolate x, we can divide both sides of the equation by -4.8283:
x = -3.2189 / -4.8283
Calculating this:
x ≈ 0.6676
Therefore, x is approximately 0.6676 when (0.008)^x = 1/25.