Solve for x, rounding to the nearest hundredth.
10 x 10^x=60
To solve this equation, we can start by taking the logarithm of both sides.
log(10 x 10^x) = log(60)
Applying the logarithm property, we can separate the terms:
log(10) + log(10^x) = log(60)
Simplifying further:
1 + xlog(10) = log(60)
Since log(10) = 1, we can substitute this value:
1 + x(1) = log(60)
1 + x = log(60)
Next, we can subtract 1 from both sides:
x = log(60) - 1
Using a calculator, we can find that log(60) ≈ 1.78.
Therefore,
x ≈ 1.78 - 1
x ≈ 0.78