Solve equation
2log10^x - 3log10^2 + log10^32 = 2
log 10^2x - log10^6 + log 10^32 = 2
log 10^ (2x*26) = 2
52 x = 10^2 = 100
x = 100/52 = 25/13
10^(2x) * 10^32 / 10^6 = 10^2
2x + 32 - 6 = 2
x = -12
Helpful thanks
To solve the equation:
2log10^x - 3log10^2 + log10^32 = 2
We can simplify the equation using the properties of logarithms.
Recall that the property of logarithms states that log base a of x raised to the power of y is equal to y times log base a of x.
Using this property, we can rewrite the equation:
log10^(x^2) - log10^(2^3) + log10^32 = 2
Now, we can apply another property of logarithms, which states that the difference of logarithms is equal to the logarithm of the quotient.
log10^(x^2 / (2^3)) + log10^32 = 2
Now, let's simplify further:
log10^(x^2 / 8) + log10^32 = 2
Next, we can apply another property of logarithms, which states that the sum of logarithms is equal to the logarithm of the product.
log10^((x^2 / 8) * 32) = 2
Simplifying the right side:
log10^(x^2 / 8 * 32) = 2
Now, we can simplify the expression inside the logarithm:
log10^(x^2 / 256) = 2
Since the base of the logarithm is 10, we can rewrite the equation as an exponential equation:
10^2 = x^2 / 256
Simplifying:
100 = x^2 / 256
We can further simplify by multiplying both sides by 256:
256 * 100 = x^2
25600 = x^2
Finally, we can take the square root of both sides to solve for x:
x = ± sqrt(25600)
Therefore, the solutions to the equation are x = ± 160.