Solve:
3 log 10^x = 4.2
the 10 is underneath the log
I got a weird number in scientific notation.
2.511... X 10^9
To solve the equation 3 log 10^x = 4.2, where the 10 is the base of the logarithm, we need to isolate x.
Step 1: Divide both sides by 3 to get rid of the coefficient:
log 10^x = 4.2 / 3
Step 2: Simplify the right side of the equation:
log 10^x = 1.4
Step 3: Rewrite the equation in exponential form:
10^(log 10^x) = 10^1.4
Step 4: Since the logarithm and exponential functions are inverses of each other, the base and the exponent cancel out on the left side:
10^x = 10^1.4
Step 5: Since the base is the same on both sides, we can equate the exponents:
x = 1.4
So the solution to the equation is x = 1.4.
To solve the equation 3 log 10^x = 4.2, we can start by using the properties of logarithms to isolate the variable x.
First, we can simplify the left side of the equation by using the logarithmic identity log a^b = b * log a. In this case, we can rewrite log 10^x as x * log 10, but the log 10 simplifies to 1, so we are left with x.
Therefore, the equation becomes:
3x = 4.2
To solve for x, we divide both sides of the equation by 3:
x = 4.2 / 3
Evaluating this expression, we get:
x ≈ 1.4
So, the solution to the equation 3 log 10^x = 4.2 is x ≈ 1.4.
Now, if you got a weird number in scientific notation, such as 2.511... × 10^9, it seems that there might have been an error in the calculations or rounding. The correct answer is approximately 1.4, not in scientific notation. Please recheck your calculations.
not weird. Just the answer.
3 log x = 4.2
log x = 1.4
x = 10^1.4 = 25.1188
Not your answer. So, investigating your answer,
x = 2.511x10^9
since log(ab) = log a + log b,
log x = log 2.511 + log 10^9
log x = 0.4 + 9
log x = 9.4
Not sure what's going on here.