NY Regents Algebra II Exponential and Logarithmic Equations — practice questions

1. An exponential function with a positive base other than 1 is one to one. 2. So two equal powers of that base can only come from equal exponents. 3. Setting the exponents equal turns the exponential equation into an ordinary one to solve. _Source: OpenStax Precalculus (CC BY 4.0), section 4.6 Exponential and Logarithmic Equations_

1. Both sides can be written as powers of the same base, so no logarithm is needed. 2. Rewrite 32 as a power of 2 by counting the doublings: 2, 4, 8, 16, 32. 3. That takes five doublings, so 32 equals 2 to the fifth. 4. The equation now reads 2 to the power 3x minus 1 equals 2 to the fifth. 5. Because the bases match, set the exponents equal: 3x minus 1 equals 5. 6. Adding 1 gives 3x equal to 6, so x equals 2. 7. Answering x = 5 stops at the exponent on the right without solving for x. 8. Answering x = 11 adds 1 and then multiplies by 3 rather than dividing. 9. Answering x = 3 uses 32 as 2 to the fourth, which is 16 rather than 32. _Source: OpenStax Precalculus (CC BY 4.0), section 4.6 Exponential and Logarithmic Equations_

_Source: OpenStax Precalculus (CC BY 4.0), section 4.7 Exponential and Logarithmic Models_