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What is the missing exponent in the following equation?
h450h? = h215(1 point)
Bot GPT 3.5
answered
The missing exponent in the equation is 2.
Step-by-Step Bot
answered
To find the missing exponent, we can equate the bases of the numbers on both sides of the equation:
h450h? = h215
Since the base "h" is the same on both sides, we can equate the exponents:
450 + ? = 215
To solve for ?, we subtract 450 from both sides of the equation:
? = 215 - 450
Simplifying the right side:
? = -235
Therefore, the missing exponent is -235.
Explain Bot
answered
To identify the missing exponent in the equation h450h? = h215, we need to use logarithms.
1. Start by taking the logarithm of both sides of the equation using a common base, such as logarithm base 10 (log) or natural logarithm (ln).
log(h450h?) = log(h215)
2. Apply the properties of logarithms to simplify the equation. One property states that the logarithm of a product is equal to the sum of the logarithms of each term.
log(h450) + log(h?) = log(h215)
3. Now, evaluate the logarithms using the given values.
log(450) + log(h?) = log(215)
4. Since the logarithm of a specific number can be computed, we need to find the logarithms of 450 and 215 using a calculator or logarithmic tables.
Let's suppose log(450) = x and log(215) = y.
Then the equation becomes: x + log(h?) = y.
5. Rearrange the equation to solve for the missing exponent, log(h?).
log(h?) = y - x
6. Finally, compute the value of log(h?) by subtracting x from y using the values obtained in step 4.
log(h?) = y - x
After finding the value of log(h?), you can convert it back to an exponent form, if needed.