To evaluate the expression log base 32 of 8, we need to find the power to which 32 must be raised to get 8.

Step 1: Write the expression in exponential form. This gives us 32^x = 8.

Step 2: Since 32 and 8 can both be expressed as powers of 2, rewrite the equation in terms of base 2. This gives us (2^5)^x = 2^3.

Step 3: Simplify the left side of the equation by multiplying the exponents. This gives us 2^(5x) = 2^3.

Step 4: Since the bases are the same, the exponents must be equal. This gives us 5x = 3.

Step 5: Solve for x by dividing both sides of the equation by 5. This gives us x = 3/5.

So, log base 32 of 8 is 3/5.

Question

To evaluate the expression log base 32 of 8, we need to find the power to which 32 must be raised to get 8.

Step 1: Write the expression in exponential form. This gives us 32^x = 8.

Step 2: Since 32 and 8 can both be expressed as powers of 2, rewrite the equation in terms of base 2. This gives us (2^5)^x = 2^3.

Step 3: Simplify the left side of the equation by multiplying the exponents. This gives us 2^(5x) = 2^3.

Step 4: Since the bases are the same, the exponents must be equal. This gives us 5x = 3.

Step 5: Solve for x by dividing both sides of the equation by 5. This gives us x = 3/5.

So, log base 32 of 8 is 3/5.

Knowee AI · Accepted Answer

To evaluate the expression log base 32 of 8, we need to find the power to which 32 must be raised to get 8.

Step 1: Write the expression in exponential form. This gives us 32^x = 8.

Step 2: Since 32 and 8 can both be expressed as powers of 2, rewrite the equation in terms of base 2. This gives us (2^5)^x = 2^3.

Step 3: Simplify the left side of the equation by multiplying the exponents. This gives us 2^(5x) = 2^3.

Step 4: Since the bases are the same, the exponents must be equal. This gives us 5x = 3.

Step 5: Solve for x by dividing both sides of the equation by 5. This gives us x = 3/5.

So, log base 32 of 8 is 3/5.

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