How do you solve for x in the equation 10^x * (2x+1)-1000=0?

Question

please provide me with the complete solution to this.

Answer 1

The question is ambiguous but let's start with 10^(x(2x+1))-1000=0.

10^(x(2x+1))=10^3, then x(2x+1)=3, 2x^2+x-3=0, (2x+3)(x-1)=0 so x=1 or -3/2.

Let's now look at (10^x)(2x+1)-1000=0. 2x+1=10^(3-x), the solution of which is x=2.2583 approx. (using an iterative method).

Answer 2

10^x=0

10 to the power of x equals 0

Take the log of both sides

log₁₀(10^x)=log₁₀(0)

Rewrite the left side of the equation using the rule for the log of a power

x•log₁₀(10)=log₁₀(0)