Final answer:
To solve 10^{4x-5} = 375, take the log of both sides, isolate x by adding 5 and dividing by 4, and use a calculator to find the decimal value of log(375) and solve for x.
Step-by-step explanation:
To solve the equation 10⁴⁹⁵ = 375, we will first understand how to use algebraic procedures and scientific notation to simplify and solve for x.
The equation seems to have a typo, and it should likely be expressed as: 10⁴¹⁵ = 375. That is, 10 to the power of 4x - 5 equates to 375. To solve for x, we first take the logarithm of both sides, preferable in base 10 due to the base of the exponent being 10:
log(10⁴¹⁵) = log(375)
By using the property of logarithms that states log(a⁾) = b * log(a), we have:
4x - 5 = log(375)
Now that the exponent is down, we will isolate x by adding 5 to both sides and then dividing by 4:
x = (log(375) + 5) / 4
Finally, you can use a calculator to find log(375) and solve for the value of x.