Final answer:
The equation 10^x=2 can be solved by taking the logarithm of both sides, simplifying, and substituting the given value log2=0.30, yielding the solution x=0.30.
Step-by-step explanation:
Solving the Equation Using Logarithms
To solve the equation 10^x=2 given that log2=0.30, we will use the property of logarithms to rewrite the equation in a form that allows us to solve for x. First, let us take the logarithm of both sides of the equation:
log(10^x) = log(2)
By the power rule of logarithms, we can bring the exponent x down in front of the log:
x · log(10) = log(2)
Since log(10) is 1 (because 10 raised to the first power equals 10), the equation simplifies to:
x = log(2)
Using the given information that log2=0.30, we can directly substitute this value:
x = 0.30
Therefore, the solution to the equation 10^x=2 is x = 0.30.