Express both bases as powers of the same prime number.

Here is the solution to the indices problem: 2. Find the value of x which satisfies the equation: 16^x = 8^(x−1) Step 1: Express both bases as powers of the same prime number. 16 = 2⁴; 8 = 2³ Step 2: Substitute these into the equation. (2⁴)^x = (2³)^(x−1); Step 3: Apply the power rule (a^m)ⁿ = a^(mn). 2^(4x) = 2^(3(x−1)); 2^(4x) = 2^(3x−3) Step 4: Equate the exponents since the bases are the same. 4x = 3x − 3 Step 5: Solve for x. 4x − 3x = −3; x = −3; The value of x is x = −3.

Express both bases as powers of the same prime number.

Here is the solution to the indices problem: 2. Find the value of x which satisfies the equation: 16^x = 8^(x−1) Step 1: Express both bases as powers of the same prime number. 16 = 2⁴; 8 = 2³ Step 2: Substitute these into the equation. (2⁴)^x = (2³)^(x−1); Step 3: Apply the power rule (a^m)ⁿ = a^(mn). 2^(4x) = 2^(3(x−1)); 2^(4x) = 2^(3x−3) Step 4: Equate the exponents since the bases are the same. 4x = 3x − 3 Step 5: Solve for x. 4x − 3x = −3; x = −3; The value of x is x = −3.

Solved: Express both bases as powers of the same prime…

Here is the solution to the indices problem:

2. Find the value of $x$ which satisfies the equation: $16^x = 8^{x-1}$

Express both bases as powers of the same prime number.
$16 = 2^4$ $8 = 2^3$
Substitute these into the equation.
$(2^4)^x = (2^3)^{x-1}$
Apply the power rule $(a^m)^n = a^{mn}$ .
$2^{4x} = 2^{3(x-1)}$ $2^{4x} = 2^{3x-3}$
Equate the exponents since the bases are the same.
$4x = 3x - 3$
Solve for $x$ .
$4x - 3x = -3$ $x = -3$
The value of $x$ is $\boxed{x = -3}$ .

Express both bases as powers of the same prime number.

Answer

Step-by-step solution

Express both bases as powers of the same prime number.

Substitute these into the equation.

Apply the power rule $(a^m)^n = a^{mn}$ .

Equate the exponents since the bases are the same.

Solve for $x$ .

Try one yourself

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More Mathematics Questions

Express both bases as powers of the same prime number.

Answer

Step-by-step solution

Express both bases as powers of the same prime number.

Substitute these into the equation.

Apply the power rule (am)n=amn(a^m)^n = a^{mn}(am)n=amn.

Equate the exponents since the bases are the same.

Solve for xxx.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Apply the power rule $(a^m)^n = a^{mn}$ .

Solve for $x$ .