1. The solution to the first equation is x=7.
2. the solution to the second equation is x≈0.0251.
Let's start by solving each equation using inverse operations step by step:
log_10 (x+3)=1
To get rid of the logarithm, rewrite the equation in exponential form. Remember that log_b (x)=y can be rewritten as b^y =x.
So, for this equation,
log_10 (x+3)=1 can be rewritten as
10^1 =x+3.
Solve for x.
10=x+3
Subtract 3 from both sides:
x=10−3
x=7
Therefore, the solution to the first equation is x=7.
log_10 (x)+3=1.4
Move the constant term to the other side of the equation.
log_10 (x)=1.4−3
log_10 (x)=−1.6
Rewrite the equation in exponential form.
10^−1.6 =x
Calculate the value of
x≈0.0251