Solve for x over the real numbers:
10^x = 0.01
Rewrite the right hand side of the equation.
0.01 = 1/100:
10^x = 1/100
Divide both sides by common terms.
Multiply both sides by 100:
10^(x+2) = 1
Any number raised to the power zero is one. Use this to express both sides with the same bases.
Express both sides with bases 2 and 5:
2^(x+2)·5^(x+2) = 2^0·5^0
Equate exponents.
Equate exponents of 2 and 5 on both sides:
x+2 = 0 and x+2 = 0
Solve the linear equations.
All equations give x = -2 as the solution:
Answer:
x = -2
Solve for x over the real numbers:
10^x = 0.01
Rewrite the right hand side of the equation.
0.01 = 1/100:
10^x = 1/100
Divide both sides by common terms.
Multiply both sides by 100:
10^(x+2) = 1
Any number raised to the power zero is one. Use this to express both sides with the same bases.
Express both sides with bases 2 and 5:
2^(x+2)·5^(x+2) = 2^0·5^0
Equate exponents.
Equate exponents of 2 and 5 on both sides:
x+2 = 0 and x+2 = 0
Solve the linear equations.
All equations give x = -2 as the solution:
Answer:
x = -2
