How do you find the variable with an exponent on an equation?

Answer 1

Solving for a variable in the exponents involves logarithsm.

A logarithm, for example a logarithm to base 10, is related to the question, "to what power do I have to raise a number [10 in the example] to get a certain other number?"

Scientific calculators can usually calculate logarithms to base 10, and base e = 2.718... directly.

Examples:

10x = 1000 is equivalent to asking for the logarithm (base 10) of 1000. Take the logarithm of 1000 on your calculator. The result, of course, should be 3.

To calculate something like 2x = 1024, divide log(1024) / log(2) (using any base, but be consistent). The result should be 10, or close to 10 (due to rounding errors, it may not be exact).

Solving for a variable in the exponents involves logarithsm.

A logarithm, for example a logarithm to base 10, is related to the question, "to what power do I have to raise a number [10 in the example] to get a certain other number?"

Scientific calculators can usually calculate logarithms to base 10, and base e = 2.718... directly.

Examples:

10x = 1000 is equivalent to asking for the logarithm (base 10) of 1000. Take the logarithm of 1000 on your calculator. The result, of course, should be 3.

To calculate something like 2x = 1024, divide log(1024) / log(2) (using any base, but be consistent). The result should be 10, or close to 10 (due to rounding errors, it may not be exact).

Solving for a variable in the exponents involves logarithsm.

A logarithm, for example a logarithm to base 10, is related to the question, "to what power do I have to raise a number [10 in the example] to get a certain other number?"

Scientific calculators can usually calculate logarithms to base 10, and base e = 2.718... directly.

Examples:

10x = 1000 is equivalent to asking for the logarithm (base 10) of 1000. Take the logarithm of 1000 on your calculator. The result, of course, should be 3.

To calculate something like 2x = 1024, divide log(1024) / log(2) (using any base, but be consistent). The result should be 10, or close to 10 (due to rounding errors, it may not be exact).

Solving for a variable in the exponents involves logarithsm.

A logarithm, for example a logarithm to base 10, is related to the question, "to what power do I have to raise a number [10 in the example] to get a certain other number?"

Scientific calculators can usually calculate logarithms to base 10, and base e = 2.718... directly.

Examples:

10x = 1000 is equivalent to asking for the logarithm (base 10) of 1000. Take the logarithm of 1000 on your calculator. The result, of course, should be 3.

To calculate something like 2x = 1024, divide log(1024) / log(2) (using any base, but be consistent). The result should be 10, or close to 10 (due to rounding errors, it may not be exact).

Answer 2

Solving for a variable in the exponents involves logarithsm.

A logarithm, for example a logarithm to base 10, is related to the question, "to what power do I have to raise a number [10 in the example] to get a certain other number?"

Scientific calculators can usually calculate logarithms to base 10, and base e = 2.718... directly.

Examples:

10x = 1000 is equivalent to asking for the logarithm (base 10) of 1000. Take the logarithm of 1000 on your calculator. The result, of course, should be 3.

To calculate something like 2x = 1024, divide log(1024) / log(2) (using any base, but be consistent). The result should be 10, or close to 10 (due to rounding errors, it may not be exact).