n-linear equations. 30. 9^x+1=81 31. 64cdot 4^3x=16 32 2^-2x+5cdot (1)/(4)=2^x+2

Question

Answer 1

### 30.

### 31.

### 32.

Answer 2

## Step 1: Rewrite 81 as a power of 9### We can rewrite 81 as

. The equation becomes

.## Step 2: Equate the exponents### Since the bases are equal, the exponents must be equal. Therefore,

.## Step 3: Solve for x### Subtract 1 from both sides of the equation:

. This simplifies to

.## Step 4: Rewrite the equation with a common base### We can rewrite 64 and 16 as powers of 4:

and

. The equation becomes

.## Step 5: Simplify the left side using exponent rules### When multiplying exponential terms with the same base, we add the exponents:

.## Step 6: Equate the exponents and solve for x### Since the bases are equal, the exponents must be equal:

. Subtract 3 from both sides:

. Divide by 3:

.## Step 7: Rewrite the equation with a common base of 2### We can rewrite

as

and 64 as

. The equation becomes

.## Step 8: Simplify the left side using exponent rules### When multiplying exponential terms with the same base, we add the exponents:

, which simplifies to

.## Step 9: Equate the exponents and solve for x### Since the bases are equal, the exponents must be equal:

. Add

to both sides:

. Subtract 2 from both sides:

. Divide by 3:

.

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